S&P codes.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 566,
   "id": "1414684c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "%matplotlib inline\n",
    "import string\n",
    "from statsmodels.formula.api import ols# for running regression\n",
    "from statsmodels.tools.tools import add_constant#for VIF test\n",
    "from statsmodels.stats.outliers_influence import variance_inflation_factor\n",
    "from scipy.stats import chi2#for chi sq test\n",
    "import statsmodels.api as sm\n",
    "from statsmodels.tsa.stattools import adfuller\n",
    "import seaborn as sns\n",
    "import statsmodels.api as sm\n",
    "import warnings\n",
    "from mpl_toolkits import mplot3d\n",
    "from pylab import rcParams\n",
    "from scipy import stats\n",
    "from sklearn.base import TransformerMixin\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "import statsmodels.stats.diagnostic as dg\n",
    "from statsmodels.stats.stattools import durbin_watson\n",
    "from statsmodels.compat import lzip\n",
    "import statsmodels.stats.api as sms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 389,
   "id": "83915677",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Dates</th>\n",
       "      <th>SandP</th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>M1_money_supply</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>Moodys_AAA_rating</th>\n",
       "      <th>CPI</th>\n",
       "      <th>PPI</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Consumer_credit_Owned_and_securitized</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1/1/1965</td>\n",
       "      <td>86.12</td>\n",
       "      <td>30.422</td>\n",
       "      <td>160.7</td>\n",
       "      <td>3.81</td>\n",
       "      <td>4.43</td>\n",
       "      <td>31.28</td>\n",
       "      <td>31.8</td>\n",
       "      <td>4.13</td>\n",
       "      <td>87.183</td>\n",
       "      <td>4.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2/1/1965</td>\n",
       "      <td>86.75</td>\n",
       "      <td>30.611</td>\n",
       "      <td>160.9</td>\n",
       "      <td>3.93</td>\n",
       "      <td>4.41</td>\n",
       "      <td>31.28</td>\n",
       "      <td>31.9</td>\n",
       "      <td>4.19</td>\n",
       "      <td>88.152</td>\n",
       "      <td>5.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3/1/1965</td>\n",
       "      <td>86.83</td>\n",
       "      <td>31.016</td>\n",
       "      <td>161.5</td>\n",
       "      <td>3.93</td>\n",
       "      <td>4.42</td>\n",
       "      <td>31.31</td>\n",
       "      <td>31.9</td>\n",
       "      <td>4.27</td>\n",
       "      <td>88.916</td>\n",
       "      <td>4.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4/1/1965</td>\n",
       "      <td>87.97</td>\n",
       "      <td>31.151</td>\n",
       "      <td>162.0</td>\n",
       "      <td>3.93</td>\n",
       "      <td>4.43</td>\n",
       "      <td>31.38</td>\n",
       "      <td>32.0</td>\n",
       "      <td>4.28</td>\n",
       "      <td>90.047</td>\n",
       "      <td>4.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5/1/1965</td>\n",
       "      <td>89.28</td>\n",
       "      <td>31.394</td>\n",
       "      <td>161.7</td>\n",
       "      <td>3.89</td>\n",
       "      <td>4.44</td>\n",
       "      <td>31.48</td>\n",
       "      <td>32.1</td>\n",
       "      <td>4.32</td>\n",
       "      <td>90.886</td>\n",
       "      <td>4.6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Dates  SandP  Industrial_Production_Index  M1_money_supply  \\\n",
       "0  1/1/1965  86.12                       30.422            160.7   \n",
       "1  2/1/1965  86.75                       30.611            160.9   \n",
       "2  3/1/1965  86.83                       31.016            161.5   \n",
       "3  4/1/1965  87.97                       31.151            162.0   \n",
       "4  5/1/1965  89.28                       31.394            161.7   \n",
       "\n",
       "   three_Month_Tbill  Moodys_AAA_rating    CPI   PPI  three_month_CD_rate  \\\n",
       "0               3.81               4.43  31.28  31.8                 4.13   \n",
       "1               3.93               4.41  31.28  31.9                 4.19   \n",
       "2               3.93               4.42  31.31  31.9                 4.27   \n",
       "3               3.93               4.43  31.38  32.0                 4.28   \n",
       "4               3.89               4.44  31.48  32.1                 4.32   \n",
       "\n",
       "   Consumer_credit_Owned_and_securitized  Unemployment_rate  \n",
       "0                                 87.183                4.9  \n",
       "1                                 88.152                5.1  \n",
       "2                                 88.916                4.7  \n",
       "3                                 90.047                4.8  \n",
       "4                                 90.886                4.6  "
      ]
     },
     "execution_count": 389,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"D:\\\\Admission\\\\Strathclyde\\\\Syllabus\\\\CS982\\\\project\\\\stock exchange data\\\\Python file.csv\")\n",
    "df.head()\n",
    "#this is raw data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 390,
   "id": "ba47aa5d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 390,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_corr = df.corr()\n",
    "sns.heatmap(df_corr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "99a78afe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SandP</th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>M1_money_supply</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>Moodys_AAA_rating</th>\n",
       "      <th>CPI</th>\n",
       "      <th>PPI</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Consumer_credit_Owned_and_securitized</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>SandP</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.840426</td>\n",
       "      <td>0.768968</td>\n",
       "      <td>-0.658160</td>\n",
       "      <td>-0.702455</td>\n",
       "      <td>0.873418</td>\n",
       "      <td>0.838758</td>\n",
       "      <td>-0.653700</td>\n",
       "      <td>0.951414</td>\n",
       "      <td>-0.151703</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <td>0.840426</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.455151</td>\n",
       "      <td>-0.658125</td>\n",
       "      <td>-0.593308</td>\n",
       "      <td>0.971002</td>\n",
       "      <td>0.945858</td>\n",
       "      <td>-0.651450</td>\n",
       "      <td>0.919742</td>\n",
       "      <td>-0.065521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>M1_money_supply</th>\n",
       "      <td>0.768968</td>\n",
       "      <td>0.455151</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.427800</td>\n",
       "      <td>-0.469998</td>\n",
       "      <td>0.550741</td>\n",
       "      <td>0.533774</td>\n",
       "      <td>-0.427154</td>\n",
       "      <td>0.639203</td>\n",
       "      <td>0.071993</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <td>-0.658160</td>\n",
       "      <td>-0.658125</td>\n",
       "      <td>-0.427800</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.885171</td>\n",
       "      <td>-0.673230</td>\n",
       "      <td>-0.619055</td>\n",
       "      <td>0.992340</td>\n",
       "      <td>-0.732942</td>\n",
       "      <td>0.027790</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Moodys_AAA_rating</th>\n",
       "      <td>-0.702455</td>\n",
       "      <td>-0.593308</td>\n",
       "      <td>-0.469998</td>\n",
       "      <td>0.885171</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.580509</td>\n",
       "      <td>-0.513843</td>\n",
       "      <td>0.873857</td>\n",
       "      <td>-0.716429</td>\n",
       "      <td>0.319427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CPI</th>\n",
       "      <td>0.873418</td>\n",
       "      <td>0.971002</td>\n",
       "      <td>0.550741</td>\n",
       "      <td>-0.673230</td>\n",
       "      <td>-0.580509</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.986326</td>\n",
       "      <td>-0.669821</td>\n",
       "      <td>0.952290</td>\n",
       "      <td>0.058685</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PPI</th>\n",
       "      <td>0.838758</td>\n",
       "      <td>0.945858</td>\n",
       "      <td>0.533774</td>\n",
       "      <td>-0.619055</td>\n",
       "      <td>-0.513843</td>\n",
       "      <td>0.986326</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.613962</td>\n",
       "      <td>0.931611</td>\n",
       "      <td>0.143217</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <td>-0.653700</td>\n",
       "      <td>-0.651450</td>\n",
       "      <td>-0.427154</td>\n",
       "      <td>0.992340</td>\n",
       "      <td>0.873857</td>\n",
       "      <td>-0.669821</td>\n",
       "      <td>-0.613962</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.722101</td>\n",
       "      <td>0.021415</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Consumer_credit_Owned_and_securitized</th>\n",
       "      <td>0.951414</td>\n",
       "      <td>0.919742</td>\n",
       "      <td>0.639203</td>\n",
       "      <td>-0.732942</td>\n",
       "      <td>-0.716429</td>\n",
       "      <td>0.952290</td>\n",
       "      <td>0.931611</td>\n",
       "      <td>-0.722101</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.038154</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Unemployment_rate</th>\n",
       "      <td>-0.151703</td>\n",
       "      <td>-0.065521</td>\n",
       "      <td>0.071993</td>\n",
       "      <td>0.027790</td>\n",
       "      <td>0.319427</td>\n",
       "      <td>0.058685</td>\n",
       "      <td>0.143217</td>\n",
       "      <td>0.021415</td>\n",
       "      <td>-0.038154</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                          SandP  Industrial_Production_Index  \\\n",
       "SandP                                  1.000000                     0.840426   \n",
       "Industrial_Production_Index            0.840426                     1.000000   \n",
       "M1_money_supply                        0.768968                     0.455151   \n",
       "three_Month_Tbill                     -0.658160                    -0.658125   \n",
       "Moodys_AAA_rating                     -0.702455                    -0.593308   \n",
       "CPI                                    0.873418                     0.971002   \n",
       "PPI                                    0.838758                     0.945858   \n",
       "three_month_CD_rate                   -0.653700                    -0.651450   \n",
       "Consumer_credit_Owned_and_securitized  0.951414                     0.919742   \n",
       "Unemployment_rate                     -0.151703                    -0.065521   \n",
       "\n",
       "                                       M1_money_supply  three_Month_Tbill  \\\n",
       "SandP                                         0.768968          -0.658160   \n",
       "Industrial_Production_Index                   0.455151          -0.658125   \n",
       "M1_money_supply                               1.000000          -0.427800   \n",
       "three_Month_Tbill                            -0.427800           1.000000   \n",
       "Moodys_AAA_rating                            -0.469998           0.885171   \n",
       "CPI                                           0.550741          -0.673230   \n",
       "PPI                                           0.533774          -0.619055   \n",
       "three_month_CD_rate                          -0.427154           0.992340   \n",
       "Consumer_credit_Owned_and_securitized         0.639203          -0.732942   \n",
       "Unemployment_rate                             0.071993           0.027790   \n",
       "\n",
       "                                       Moodys_AAA_rating       CPI       PPI  \\\n",
       "SandP                                          -0.702455  0.873418  0.838758   \n",
       "Industrial_Production_Index                    -0.593308  0.971002  0.945858   \n",
       "M1_money_supply                                -0.469998  0.550741  0.533774   \n",
       "three_Month_Tbill                               0.885171 -0.673230 -0.619055   \n",
       "Moodys_AAA_rating                               1.000000 -0.580509 -0.513843   \n",
       "CPI                                            -0.580509  1.000000  0.986326   \n",
       "PPI                                            -0.513843  0.986326  1.000000   \n",
       "three_month_CD_rate                             0.873857 -0.669821 -0.613962   \n",
       "Consumer_credit_Owned_and_securitized          -0.716429  0.952290  0.931611   \n",
       "Unemployment_rate                               0.319427  0.058685  0.143217   \n",
       "\n",
       "                                       three_month_CD_rate  \\\n",
       "SandP                                            -0.653700   \n",
       "Industrial_Production_Index                      -0.651450   \n",
       "M1_money_supply                                  -0.427154   \n",
       "three_Month_Tbill                                 0.992340   \n",
       "Moodys_AAA_rating                                 0.873857   \n",
       "CPI                                              -0.669821   \n",
       "PPI                                              -0.613962   \n",
       "three_month_CD_rate                               1.000000   \n",
       "Consumer_credit_Owned_and_securitized            -0.722101   \n",
       "Unemployment_rate                                 0.021415   \n",
       "\n",
       "                                       Consumer_credit_Owned_and_securitized  \\\n",
       "SandP                                                               0.951414   \n",
       "Industrial_Production_Index                                         0.919742   \n",
       "M1_money_supply                                                     0.639203   \n",
       "three_Month_Tbill                                                  -0.732942   \n",
       "Moodys_AAA_rating                                                  -0.716429   \n",
       "CPI                                                                 0.952290   \n",
       "PPI                                                                 0.931611   \n",
       "three_month_CD_rate                                                -0.722101   \n",
       "Consumer_credit_Owned_and_securitized                               1.000000   \n",
       "Unemployment_rate                                                  -0.038154   \n",
       "\n",
       "                                       Unemployment_rate  \n",
       "SandP                                          -0.151703  \n",
       "Industrial_Production_Index                    -0.065521  \n",
       "M1_money_supply                                 0.071993  \n",
       "three_Month_Tbill                               0.027790  \n",
       "Moodys_AAA_rating                               0.319427  \n",
       "CPI                                             0.058685  \n",
       "PPI                                             0.143217  \n",
       "three_month_CD_rate                             0.021415  \n",
       "Consumer_credit_Owned_and_securitized          -0.038154  \n",
       "Unemployment_rate                               1.000000  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 391,
   "id": "74cf0df1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SandP</th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>M1_money_supply</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>Moodys_AAA_rating</th>\n",
       "      <th>CPI</th>\n",
       "      <th>PPI</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Consumer_credit_Owned_and_securitized</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>86.12</td>\n",
       "      <td>30.422</td>\n",
       "      <td>160.7</td>\n",
       "      <td>3.81</td>\n",
       "      <td>4.43</td>\n",
       "      <td>31.280</td>\n",
       "      <td>31.8</td>\n",
       "      <td>4.13</td>\n",
       "      <td>87.183</td>\n",
       "      <td>4.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>86.75</td>\n",
       "      <td>30.611</td>\n",
       "      <td>160.9</td>\n",
       "      <td>3.93</td>\n",
       "      <td>4.41</td>\n",
       "      <td>31.280</td>\n",
       "      <td>31.9</td>\n",
       "      <td>4.19</td>\n",
       "      <td>88.152</td>\n",
       "      <td>5.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>86.83</td>\n",
       "      <td>31.016</td>\n",
       "      <td>161.5</td>\n",
       "      <td>3.93</td>\n",
       "      <td>4.42</td>\n",
       "      <td>31.310</td>\n",
       "      <td>31.9</td>\n",
       "      <td>4.27</td>\n",
       "      <td>88.916</td>\n",
       "      <td>4.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>87.97</td>\n",
       "      <td>31.151</td>\n",
       "      <td>162.0</td>\n",
       "      <td>3.93</td>\n",
       "      <td>4.43</td>\n",
       "      <td>31.380</td>\n",
       "      <td>32.0</td>\n",
       "      <td>4.28</td>\n",
       "      <td>90.047</td>\n",
       "      <td>4.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>89.28</td>\n",
       "      <td>31.394</td>\n",
       "      <td>161.7</td>\n",
       "      <td>3.89</td>\n",
       "      <td>4.44</td>\n",
       "      <td>31.480</td>\n",
       "      <td>32.1</td>\n",
       "      <td>4.32</td>\n",
       "      <td>90.886</td>\n",
       "      <td>4.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>675</th>\n",
       "      <td>4141.18</td>\n",
       "      <td>99.230</td>\n",
       "      <td>18915.7</td>\n",
       "      <td>0.02</td>\n",
       "      <td>2.90</td>\n",
       "      <td>266.832</td>\n",
       "      <td>217.9</td>\n",
       "      <td>0.11</td>\n",
       "      <td>4241.604</td>\n",
       "      <td>6.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>676</th>\n",
       "      <td>4167.85</td>\n",
       "      <td>99.850</td>\n",
       "      <td>19192.9</td>\n",
       "      <td>0.02</td>\n",
       "      <td>2.96</td>\n",
       "      <td>268.551</td>\n",
       "      <td>224.9</td>\n",
       "      <td>0.10</td>\n",
       "      <td>4276.989</td>\n",
       "      <td>5.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>677</th>\n",
       "      <td>4238.49</td>\n",
       "      <td>100.340</td>\n",
       "      <td>19238.2</td>\n",
       "      <td>0.04</td>\n",
       "      <td>2.79</td>\n",
       "      <td>270.981</td>\n",
       "      <td>228.5</td>\n",
       "      <td>0.09</td>\n",
       "      <td>4315.176</td>\n",
       "      <td>5.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>678</th>\n",
       "      <td>4363.71</td>\n",
       "      <td>101.187</td>\n",
       "      <td>19401.7</td>\n",
       "      <td>0.05</td>\n",
       "      <td>2.57</td>\n",
       "      <td>272.265</td>\n",
       "      <td>231.2</td>\n",
       "      <td>0.10</td>\n",
       "      <td>4332.450</td>\n",
       "      <td>5.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>679</th>\n",
       "      <td>4454.21</td>\n",
       "      <td>101.595</td>\n",
       "      <td>19677.7</td>\n",
       "      <td>0.05</td>\n",
       "      <td>2.55</td>\n",
       "      <td>273.012</td>\n",
       "      <td>232.9</td>\n",
       "      <td>0.10</td>\n",
       "      <td>4346.829</td>\n",
       "      <td>5.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>680 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       SandP  Industrial_Production_Index  M1_money_supply  three_Month_Tbill  \\\n",
       "0      86.12                       30.422            160.7               3.81   \n",
       "1      86.75                       30.611            160.9               3.93   \n",
       "2      86.83                       31.016            161.5               3.93   \n",
       "3      87.97                       31.151            162.0               3.93   \n",
       "4      89.28                       31.394            161.7               3.89   \n",
       "..       ...                          ...              ...                ...   \n",
       "675  4141.18                       99.230          18915.7               0.02   \n",
       "676  4167.85                       99.850          19192.9               0.02   \n",
       "677  4238.49                      100.340          19238.2               0.04   \n",
       "678  4363.71                      101.187          19401.7               0.05   \n",
       "679  4454.21                      101.595          19677.7               0.05   \n",
       "\n",
       "     Moodys_AAA_rating      CPI    PPI  three_month_CD_rate  \\\n",
       "0                 4.43   31.280   31.8                 4.13   \n",
       "1                 4.41   31.280   31.9                 4.19   \n",
       "2                 4.42   31.310   31.9                 4.27   \n",
       "3                 4.43   31.380   32.0                 4.28   \n",
       "4                 4.44   31.480   32.1                 4.32   \n",
       "..                 ...      ...    ...                  ...   \n",
       "675               2.90  266.832  217.9                 0.11   \n",
       "676               2.96  268.551  224.9                 0.10   \n",
       "677               2.79  270.981  228.5                 0.09   \n",
       "678               2.57  272.265  231.2                 0.10   \n",
       "679               2.55  273.012  232.9                 0.10   \n",
       "\n",
       "     Consumer_credit_Owned_and_securitized  Unemployment_rate  \n",
       "0                                   87.183                4.9  \n",
       "1                                   88.152                5.1  \n",
       "2                                   88.916                4.7  \n",
       "3                                   90.047                4.8  \n",
       "4                                   90.886                4.6  \n",
       "..                                     ...                ...  \n",
       "675                               4241.604                6.1  \n",
       "676                               4276.989                5.8  \n",
       "677                               4315.176                5.9  \n",
       "678                               4332.450                5.4  \n",
       "679                               4346.829                5.2  \n",
       "\n",
       "[680 rows x 10 columns]"
      ]
     },
     "execution_count": 391,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = df.drop(columns=['Dates'])\n",
    "df1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "7d73e689",
   "metadata": {},
   "outputs": [],
   "source": [
    "Dates = df.Dates\n",
    "SandP = df.SandP\n",
    "IPI = df.Industrial_Production_Index\n",
    "M1 = df.M1_money_supply\n",
    "Tbill = df.three_Month_Tbill\n",
    "AAA = df.Moodys_AAA_rating\n",
    "CPI = df.CPI\n",
    "PPI = df.PPI\n",
    "CDrate = df.three_month_CD_rate\n",
    "Credit = df.Consumer_credit_Owned_and_securitized\n",
    "Unemp = df.Unemployment_rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d1c82103",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#plt.scatter(y=SandP,x=IPI)\n",
    "#plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 392,
   "id": "2e60c3a5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 392,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.boxplot(column=['three_Month_Tbill','three_month_CD_rate','Moodys_AAA_rating'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "519f6ad5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'S&P 500')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(SandP)\n",
    "plt.xlabel(\"01/1965 to 08/2021 - 680 observations\")\n",
    "plt.ylabel(\"index value\")\n",
    "plt.title(\"S&P 500\", weight = \"bold\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "cdc2dd83",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Consumer price index')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(CPI)\n",
    "plt.xlabel(\"01/1965 to 08/2021 - 680 observations\")\n",
    "plt.ylabel(\"index value\")\n",
    "plt.title(\"Consumer price index\", weight = \"bold\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "38492e94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Credit owned & securitized')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Credit)\n",
    "plt.xlabel(\"01/1965 to 08/2021 - 680 observations\")\n",
    "plt.ylabel(\"$ Billion\")\n",
    "plt.title(\"Credit owned & securitized\", weight = \"bold\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "93dfc77a",
   "metadata": {},
   "outputs": [],
   "source": [
    "#we'll pplot two or three variables and show that it is clearly visible that they all are non stationary time series\n",
    "#so we'll directly compute first order differencing and then apply ADF test"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2921d19d",
   "metadata": {},
   "source": [
    "### First order differencing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 393,
   "id": "c93b8e5b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SandP</th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>M1_money_supply</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>Moodys_AAA_rating</th>\n",
       "      <th>CPI</th>\n",
       "      <th>PPI</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Consumer_credit_Owned_and_securitized</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.63</td>\n",
       "      <td>0.189</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.12</td>\n",
       "      <td>-0.02</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.06</td>\n",
       "      <td>0.969</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.08</td>\n",
       "      <td>0.405</td>\n",
       "      <td>0.6</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.030</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.764</td>\n",
       "      <td>-0.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.14</td>\n",
       "      <td>0.135</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.070</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.01</td>\n",
       "      <td>1.131</td>\n",
       "      <td>0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.31</td>\n",
       "      <td>0.243</td>\n",
       "      <td>-0.3</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.100</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.839</td>\n",
       "      <td>-0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>675</th>\n",
       "      <td>230.67</td>\n",
       "      <td>0.068</td>\n",
       "      <td>246.3</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>-0.14</td>\n",
       "      <td>2.039</td>\n",
       "      <td>2.9</td>\n",
       "      <td>0.01</td>\n",
       "      <td>18.714</td>\n",
       "      <td>0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>676</th>\n",
       "      <td>26.67</td>\n",
       "      <td>0.620</td>\n",
       "      <td>277.2</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.06</td>\n",
       "      <td>1.719</td>\n",
       "      <td>7.0</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>35.385</td>\n",
       "      <td>-0.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>677</th>\n",
       "      <td>70.64</td>\n",
       "      <td>0.490</td>\n",
       "      <td>45.3</td>\n",
       "      <td>0.02</td>\n",
       "      <td>-0.17</td>\n",
       "      <td>2.430</td>\n",
       "      <td>3.6</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>38.187</td>\n",
       "      <td>0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>678</th>\n",
       "      <td>125.22</td>\n",
       "      <td>0.847</td>\n",
       "      <td>163.5</td>\n",
       "      <td>0.01</td>\n",
       "      <td>-0.22</td>\n",
       "      <td>1.284</td>\n",
       "      <td>2.7</td>\n",
       "      <td>0.01</td>\n",
       "      <td>17.274</td>\n",
       "      <td>-0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>679</th>\n",
       "      <td>90.50</td>\n",
       "      <td>0.408</td>\n",
       "      <td>276.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-0.02</td>\n",
       "      <td>0.747</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.00</td>\n",
       "      <td>14.379</td>\n",
       "      <td>-0.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>680 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      SandP  Industrial_Production_Index  M1_money_supply  three_Month_Tbill  \\\n",
       "0       NaN                          NaN              NaN                NaN   \n",
       "1      0.63                        0.189              0.2               0.12   \n",
       "2      0.08                        0.405              0.6               0.00   \n",
       "3      1.14                        0.135              0.5               0.00   \n",
       "4      1.31                        0.243             -0.3              -0.04   \n",
       "..      ...                          ...              ...                ...   \n",
       "675  230.67                        0.068            246.3              -0.01   \n",
       "676   26.67                        0.620            277.2               0.00   \n",
       "677   70.64                        0.490             45.3               0.02   \n",
       "678  125.22                        0.847            163.5               0.01   \n",
       "679   90.50                        0.408            276.0               0.00   \n",
       "\n",
       "     Moodys_AAA_rating    CPI  PPI  three_month_CD_rate  \\\n",
       "0                  NaN    NaN  NaN                  NaN   \n",
       "1                -0.02  0.000  0.1                 0.06   \n",
       "2                 0.01  0.030  0.0                 0.08   \n",
       "3                 0.01  0.070  0.1                 0.01   \n",
       "4                 0.01  0.100  0.1                 0.04   \n",
       "..                 ...    ...  ...                  ...   \n",
       "675              -0.14  2.039  2.9                 0.01   \n",
       "676               0.06  1.719  7.0                -0.01   \n",
       "677              -0.17  2.430  3.6                -0.01   \n",
       "678              -0.22  1.284  2.7                 0.01   \n",
       "679              -0.02  0.747  1.7                 0.00   \n",
       "\n",
       "     Consumer_credit_Owned_and_securitized  Unemployment_rate  \n",
       "0                                      NaN                NaN  \n",
       "1                                    0.969                0.2  \n",
       "2                                    0.764               -0.4  \n",
       "3                                    1.131                0.1  \n",
       "4                                    0.839               -0.2  \n",
       "..                                     ...                ...  \n",
       "675                                 18.714                0.1  \n",
       "676                                 35.385               -0.3  \n",
       "677                                 38.187                0.1  \n",
       "678                                 17.274               -0.5  \n",
       "679                                 14.379               -0.2  \n",
       "\n",
       "[680 rows x 10 columns]"
      ]
     },
     "execution_count": 393,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2 = df1.diff()\n",
    "df2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 394,
   "id": "b8282371",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SandP</th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>M1_money_supply</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>Moodys_AAA_rating</th>\n",
       "      <th>CPI</th>\n",
       "      <th>PPI</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Consumer_credit_Owned_and_securitized</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.63</td>\n",
       "      <td>0.189</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.12</td>\n",
       "      <td>-0.02</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.06</td>\n",
       "      <td>0.969</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.08</td>\n",
       "      <td>0.405</td>\n",
       "      <td>0.6</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.764</td>\n",
       "      <td>-0.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.14</td>\n",
       "      <td>0.135</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.07</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.01</td>\n",
       "      <td>1.131</td>\n",
       "      <td>0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.31</td>\n",
       "      <td>0.243</td>\n",
       "      <td>-0.3</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.839</td>\n",
       "      <td>-0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-4.24</td>\n",
       "      <td>0.244</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.09</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.13</td>\n",
       "      <td>0.3</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>0.944</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   SandP  Industrial_Production_Index  M1_money_supply  three_Month_Tbill  \\\n",
       "1   0.63                        0.189              0.2               0.12   \n",
       "2   0.08                        0.405              0.6               0.00   \n",
       "3   1.14                        0.135              0.5               0.00   \n",
       "4   1.31                        0.243             -0.3              -0.04   \n",
       "5  -4.24                        0.244              0.5              -0.09   \n",
       "\n",
       "   Moodys_AAA_rating   CPI  PPI  three_month_CD_rate  \\\n",
       "1              -0.02  0.00  0.1                 0.06   \n",
       "2               0.01  0.03  0.0                 0.08   \n",
       "3               0.01  0.07  0.1                 0.01   \n",
       "4               0.01  0.10  0.1                 0.04   \n",
       "5               0.02  0.13  0.3                -0.01   \n",
       "\n",
       "   Consumer_credit_Owned_and_securitized  Unemployment_rate  \n",
       "1                                  0.969                0.2  \n",
       "2                                  0.764               -0.4  \n",
       "3                                  1.131                0.1  \n",
       "4                                  0.839               -0.2  \n",
       "5                                  0.944                0.0  "
      ]
     },
     "execution_count": 394,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df3 = df2.iloc[1: , :]\n",
    "df3.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "f48743cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'CPI after differencing')"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(df2.CPI,color=\"green\")\n",
    "plt.xlabel(\"02/1965 to 08/2021 - 679 observations\")\n",
    "plt.ylabel(\"index value\")\n",
    "plt.title(\"CPI after differencing\", weight = \"bold\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "8cca323e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Credit after differencing')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(df2.Consumer_credit_Owned_and_securitized,color=\"green\")\n",
    "plt.xlabel(\"02/1965 to 08/2021 - 679 observations\")\n",
    "plt.ylabel(\"$ Billion\")\n",
    "plt.title(\"Credit after differencing\", weight = \"bold\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "8432202d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'S&P 500 after differencing')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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f387Xy78u9/UmL53MytyV7PHYHixat6jM5x/98tF0e6pbaN+L1srJy+HwMYeH1b3wvQtp8WCLUn8zvzsrUmmoElEUpUx4/v9N2zcBVik0vr8x139yPRDuGln410J+/etXbpx0Y6gs1voUEF+vuDLIycvh942/l1ovUsl5DfC9U+/lkBcOKfX89xe8XyKL7qTFk3hn3juh/ddmvcbi9Yt56senAJuKZOO2jaVe22PZxmWhbc+FNf/P+SXqjZkxhpwtOWVyZ2WlZ4Udq51RO265yoMqEUXZSfAazY3bbaPmNW4Pf/dw2HGAY145hi5PdOHBbx4Mlb2/4H1+Wf1L1OsXFBXw1fKvWPjXQt6d/27I8hk1bRRyt1BQVIAxhqUblobOWZu3Nuwa2wu2R/X/R6PbU91o/2j7sLItO7bwn2/+E6bYIifz7SjcEXV8KJLVm1czcNxAjn3l2LDyY145hlPeOCW0790vXdJZvnE5J752Iue/e37o+D+n/DO+hwKu+OgKAAzFMtbJqBP2zjZs21DqdTxLJFKJVEV4L6gSUZSdBq/XumXHFrbu2Bo2kLtk/ZKw3ry/ofe48dMb6fF0j5jXP/SFQ+n8RGdOfv1kzhh/BgA3TLohdN8RU0fQ4b8dWPjXQn744wda/qclr80qzifVfWR36v6rbG6WnC05QHiD+uDXD3LDpBt4/ufnQ2WRltKOoh0l3EGvznqVz34rOVbiXfub37+JKcuPK38ErNWXuz0XCLck7vjijrhnzHtRWp7lCFC/Vn26P9U9tL9i04qY1/C7s6oinDcIVSKKspPgbzBfnvlymBLp+FhHLvngkriuE811FBmdtHj94rD97QXbuX3y7QCs37ae71Z8B8DXvxePRwSNJfy55U/+8fE/wuRdvG4xF713Udg9f1n9S2jf6737ZY1UIvmF+SXcQWe/fTZHv3x0CRn8bqwiU8T8P+eHlISft+a9BdgFn7qP7F7iOJRtlrgxJkw5ZqZnhpQmwO+bYrvx/JMNVYkoilIu/A1m3cy6UecelEb7R9sHjn/4G7cgvl3xbWh7y44toUa4fq36Jer63Uz/nPJPnvzxSV765aVQ2YXvXcgLM17gxz9+DIWuvvjLi2Tdm8Xo6aPZpc4uAKzbui50TmRiyYKigjDF6ldSh485PExB+ZXIkvVL2OvJvTjwuQOjPuucnDlRj5XlvS/fuDzsGSLHdVbmrox5vlDsssrKyIpRs/LQyYaKUgGMnTmWWum1OK3baZV+r6UbllIvsx7N6zUHrPJIT0sPaxS3FWwr13oTm7ZvCjXUHqW5VpZtKB403rJjS6hhDlIiG7ZtoEmdJgDUyawDWIvEf3/vOl4P20tnMnvtbHq17gXAum3FDXAJd1bhjjDF6nfhfbnsS8bMGMObc9+ked3mnNm9eC0Qb82OWIrCT2TDv3XH1rjHYrL/mx22H2nFxPMbes+dLEtElYiiVADnvHMOAKZb2ZdALSsd/tuBzLRM8m+3SqPpA01pVLsRnZt2DtXJy88rlxLZuG1jmZWIf0B4/db1oQH+wqJCthdsD5s9viZvTUiJePfxBuqhuDe/avOqUOPoXc+7JhCWfThyYD1vR16YJRLpSluZu5JPf/sUgNdmF4/bfLn8y5jPGUlk7rFtBdsSDof2frPjOx3Pxws/LnWCo4ioElGUnZUPf/2Q5nWbs3/b/Sv82qFIrG0byc3PJTc/N6yR9wbXEyUoKshvKfjxXCp+JeIpVbCuotojwsNN1+atZc9mewLQoFYDoNg1lZefF3qWayZcE5pE5ykZQUKNqz8zbtCYiN9NtWbzmrDjfsURKVt52FqwtcxrtrRp0IZT9zqVJ398EoDdGu0GRM8iUCejDlsLtiIUK5HI6KyqQsdEFKWSGPDaAA547oBKvYcXLRTJlh1b+O/3/034uv5ev0dpA8ZrtwQ3vpFzL8AqikmLJ3HtxGtDjaA35jJl2ZRQhNP6betD255iKzJFISU6ddlUhn4wFAhebOvpaU8XyxehHH7969dAeXPyYo/9lMbWHVvLbIk0rt2YNEkLnefN8Yg22dA/B6TAFFsiR3Y4EoDuLYIH/SsDVSJKjWXyksmMnj66Qq8Zry+8rNf7avlXnPbmaTz49YNhx2757JbA8/J25DHpt0kJ3zdoAl2ke8w/qAsle/qhawUopPFzx3P+u+fzyHePMHHxRMCOeeRuz+WPTX8AcHRHG0XlNf5eRFZBUUFYlNYzPz1DYVFhYDCAN0cGrAsNYMftsSfwlRZAUBqrNq+KuQAVwLUHXBu2X79W/VCUFVhLA6JbIp5r0O/OysrI4rPzPqPg9gJmXDYjUfHLjCoRJeWIdwbw6s2ro7pYwDaykSv2XTfxOlo82ILF6xZz5EtHctmHl4WOFZkiHvrmobBoGY/XZr0WNXWGv/HMzbcRSdH++Tdu21jqLGQv2d+sNbNIuycNuVs49IVDGT93PDd+WjzD/KFvH4pqiXihqImyftv6EmWxFlUC29g3rt24RHnQb/T8jOdZtXkVUDw34/dNv9PwvoYs37gcgOsPvD7wPqOmjyqRF2tH0Y4SSuSZAc+UkK9RVqOYmX3TJb2EFfHcSeHZi7MbZ0c9H+CM8Wfw3oL3YtZpVb9V2P62gm1hi0t5lka0vyOvrt+dlZmWaZ8hLT00i70qqHZKRET6i8gCEVkkIjcnW56dgfzC/ArvQSdKTl4Oje9vzN8/+nupdVs/1JoWD7bAGMOUpcUukIKiAs5++2w6PtaRZg82C81XABj902hytuTQ8+meobLN+Zv5YMEHfL38a66fdD1DPxjKp799yvw/5/P+gvfp/lR3znr7LA554RByt+dSZIo4/c3T6f9KfwqLCmn1UHGDkJOXw0+rfgoMzVyZu5LG9zfm2onXhg0iR9LovkYMHDcwLAdWEN4kvyC8hjhRLnzvwhJlQe6s1ZtXhxTn2ry1NKndpESdqcunxrxXpMKasHgCTes0ZbfGu0U9Z8KiCWH7+YX5JXr/l/QKnxezNm9tiWABj0ZZjfjmom8CI8k6NO5Au4btQvsndjoxqlwe83LmxTzepkGbsP3N+ZsDlUi0DodfSYSUSHpmqXJVBtVKiYhIOvAkcBzQFThTRLomU6ZYg5ejpo3iuZ/KtgbDms1rmJczj1HTRoX90xpjuGnSTXy1/KtQWX5hPq/MfKWED3dt3lqMMWzdsTXsH2v15tXs/+z+3Pb5bUxdZv+xc7fnUndEXYZ/NjxuGddtXcf0ldM5753zmJszF2NMSAmt27qOtXlr2bR9E8s2LGPWmlmc8OoJfLH0C96e9zZrNq/h+xXfl+jtbc7fzMu/vMwva2zajZHTRjJ25ljumXIPt3x2C39s+iOwYTQYnv/5eY548Qj+NfVfLFm/hJlrZvLqrFdDIZ0HPncg/576by774LKQf95r+MD+TieNO4nDxhwG2F58v5f7sdeTezFw3MCwUM+G9zUk/Z503pz7JhMXTyzRmN35xZ30Ht2bSz+4NFTW/anuNLqvEQ98/QAAT/z4BLs/tjvLNy5n8BuDmbhoIgNeG8DUZVNZvXk1YBtJ7128OOjFuH+biqTIFDFnbfGzB0V7tX6odWg7Nz83rBHef9f92WOXPcocJTZt5TRaN2hdoqGNRX5hfqgxbVW/VahX7mf15tWhiLBIshtnc2C7AwOVSFZGVlhqkoPaHVSqPP5Z6EE0rds0bD8vPy9MMZRmiQS5s5K1dkp1i87qCywyxvwGICLjgIHA3Iq+0bvz32XZhmVkpGUwfdV0VuaupGOTjtTLrMeavDU80O8BJiyaEOqxnbrXqTTIakCzOnat6tV5q0Px5o989wjbC7dz6l6ncnq30zn/3fP5e5+/07FJR9bmreWQ9ofw8cKPOarjUfQY1SPkNrjioys4bLfDeGbAMwybMIwJiybwwDcPcEGPC9icv5nxc8cDNpJj3pXzyNuRx/BPh/Psz89yVd+rePyHxzmt62k8dMxDLFy3kKNeOgqAH/74gRFTR3Ddgdfx0LcPAXD/1/eTLumMnzeeVvVbMf/P+Tx0zEP036M/ExZN4PDdDmfZxmV0adqFvZ7ci7+2WjfR9398T+2M2sxcM5NerXvx06qfADtQ6I/w+Xjhx4D9Z126YSmn7nUqw/YfxrM/P8uKTSvYo8kejP5pNAe2LZ7g5Y/w+fdX/wbgrsPvon2j9uzbat/QMW8m9oipIxgxdURg4rlbPg8eO/DeRyy6NO1Cw6yGga6jSLeRZz14oaNQPN/AP9C9ftt6dnt0t7BrfL3867Be+aJ1izhlr1M4b9/zwvIzRfLZeZ/xyeJPuP/r+2M+B1iXRzyr5QHcM+WesIWVSnNnQfGcD4BnT3qWf039V0IZb3epswsNsxpyQNsDwizJaOwo3BEaWB95wkgG7TmoRJ05OXMY3HVw4Pn1atUDiue01M2sG7Jss9Kzwjo9B7QtPVjiz63R3axQcu2PaO6saL+VN37id2epEomPXQF/HoAVQIXHTxpjGDZhWFjPt3HtxqEBQLBpJTwaZjWM6YP2GpH7v74/9I/+94/jcNfUb82Xy76kyxNdwsrHzBgTtr9s4zLq/qsugoR6TI//8DgAb859kzfnvhlW3wsP9BSIx7+++hdQHLVy7jvnliqjP8LFUyAQHiJ6We/LaNewHbdNvi1kHbw1762wd/b5ks8BO+t5lzq70H+P/rw661XGnjKWf3/1b2avnQ3AXVPuiinP7k12D0vHcdwex/G/Rf8L7Xdr3o1erXvx8syXadewHb9v+r1UJdKpaSfO2fschrw1pMSxjxZ+FPPcshDp1lm0bhEDOg8A4PXBr/PQtw9x+G6HhyVNBNvzvu7A60J/WzcffDP3fX1f4D1qZ9RmR358SuSTxZ+E7cdjUfjDTBtlNSqx2l4k7Ru1D7Qwvcb8rO5nxaVE/JaIf4A6kr1b7B1YXi8zXIk0r9s8lHE3KyMrzN3bvlFxMsh0SQ+MCosci4vEC2sGuLTXpVzQ44Iwq9ZTxtEskSB3VrKUSLVyZwFBaSlLOPNFZKiITBORaTk5ZY+0EBFmXDaD/51tG5+z9z6bpcOW8tTxT5Wo++GZH7L+pvVsvHkjj/V/jMVXL2avZnuFji8ZtoSLe17M5+d9Hoq48Ezt8/Y9r8T1xp06jqXDlrLuxnUsGbaEa/a/huM7HR86vuGmDXx45ocMP2Q4l/S8hMnnT2aflvsAtjfl/+MMonX91uQOzw0NWh7V4Sge7Pcgi65axJiBY3j1lFcB6Nq8K+0btefY3Y9l+CHD6dK0C1npWdRKr8Vj/R9jzt/nhL2P6w+8nmN3P5bJ50+mYVbDMFfE4K6DufWwW/nknPBGKRpPHf8UY08Zi7nTcNbeZzHiyBGB9do3as9/+v2HI7KP4L6j7mPUCaO4/iD7XH/v83eK7ijio7M+onfr3sXvd/A4Tut6GvVr1ee2w24DrBL2v2M/Dx/zMM8MeIbTu50eVn7s7seGLEmP1059jRsOuoGRJ4zkmN2PKRGB4/HIsY+EtqcPnc7rg1/n8t6XB9b1GuHTu53O95d8z/1H38/oE0eHQjnBNnwNsop/95sPuZndm+wOwE9Df6Jfx36hY1kZWbxy8iscs/sxgffzExmaG48lkpWRxUuDXqJpnaa0qNeixABv1+bh3uer+l4V2r7hoOIxHq9R9xrT5nWbx7zv8M+Gc/xY+xv6G9NIheLNTYkk0hJpUa9F8TP5LJEF/1gQ9kyjBwRH9/k7nEH4LZHRA0ZzULuDwmQtzZ3VtmFbQN1ZibACaOfbbwuUGME0xowGRgP06dMnoRHjJnWa0H+P/vz6j1/JbpxNZnomV+x3BUO6D+G7Fd9Rv1Z9sjKy6LtrX8D+UVy1v/2HmHvlXDZt38TWHVtpWb8lz570LAC/XvUrRaYIYwzvL3ifi3tdzBV9rqBORh32e2Y/dhTt4ITOJ4T5ZR/pbxucvPw85v85n0a1G3FC5xM4ofMJoTpTLpiCIKFJWZe+fyljZ41lygVTeGf+OyFX0MgTRjKwy0DS09K5su+V/LjyR8YMGhP6g9x9F9vwDNxzIHUy6oSlkv7XUdZK2V6wPZSjp2vzrjTIakCdjDqc2vXUUN1FVy0iKyOLRvdZebx31G/3fqy6bhUbtm1gz2Z7Infb699+2O0UFBXwt+y/MXLaSE7Zqzj1NsBJXU5i6oVTObDtgZw07iQ+XvgxOTfk0Lh2YzLSMrjuoOtCdXcU7mDvFnvTo1WPkPwTz5nITZ/ehDGGbs270b1FdzbdvCnMcmpTvw2vD36dL5d9SeemnVm9eTUHtj2QAV0GhOo8O+DZkOvs7L3P5rEfHuO39b/RtE5T/rzRui+GdLfWyuV9LscYw6G7HcryjctZsWkFe7fYm8a1G3NUx6N4YcYLPHLsI/Rq3YterXuxe5PdGTV9FFnpWWy5dQs7CncwYuqIEoPDIsKlvS/l0t6Xht5fvcx6YRZAZnpmaJC1VnotPjzrQ85951zemPMGtTNqc/Y+ZzO46+ASEwAjmbV2Vth+vJbIufuey7n7BluxJ3Q6gbk5xd7n1vWLx1Qe6PcA01dN5/Mln4cada8xLa2B9E8c9NfNTM+ksKDYUgga+IeSlog/yqx2Ru2Qhe+950/P/ZQ2DdpEjY4rjQZZDejWvBudmnYKlcUbndWvYz/2abkPXyz9Qt1ZCfAj0ElEOgB/AEOAsyrzhv4fGaxyOa7TcaWe1zCrYQm/p9dYAyGF4/lXZ1w+g59W/RQ4sAe2p9S7Te/AY5FhlaMHjOapE54iMz2Tnq17krs9l8v6XBY2ASm7cTZfXPBF4PVirYgWmeTtnH3OKVHHy+k06dxJfPP7N2HvoVX9VqHwxnfOeIcnf3ySu4+4O9Tg99u9X4nrARzS3i4q9OoprzInZw7N6jYLrJeZnsnB7Q8OK2tat2lIkXuISNgga+PajTm92+klLA4/F/e6mMFdB/Pm3Dc5teupIZfmEdlHBNYXkUDfPMAvl4ev29GjVQ8aZjWkSe0mpEkaWRlZ3PO3e6LK4qd+rfphCj8zLZPLe1/ONROvoVX9VtRKrxWyUL1GMCsji1EnjOLyj4ItoCAio7OC1quI/PuIjPrzGmuPyMFzzwKon1k/9CxAmUJW/XUjG1a/xebH8xJ4/3/+sZ2sjGJLxHu+ozra8cXIJWkh2MV1ZvczubjnxaEMwg1qNWD232eH1fErEU+eoOisnq16ho3RRIb4VjXVSokYYwpE5B/ARCAdeN4YE1+WtBSna/OuJUz9RBGRUE80Iy2Dx49/vEKuW1aO7nh0aMJYEIP2HBS1kY1Go9qN4oqOiQd/rzRofkO0+3vWgddQHNzu4FinxEV6WjoDOg8oNaoniMicSRlpGVy9/9Vc2ffKUCPqffuDDuJxafmJ5c7yz7b2E6loIhvdyCilFnWtEvEskUj548FfN/LdeMr05D1P5p3575Q4xzvuNeJgFa+nDCPlaNOgDUO6D2Hc7HGhsplXzAxbBhes+/Oojkfx8VkfMzdnbmA4blB0VqEpDFRK3nv1u7Oqcm6In+o2JoIx5mNjTGdjzO7GmGBnuaLEgb9Bi1eJ+PEGT/2JD8vDmEFjeOeMd0qvGEFkQy0iiEhYg+dt+y0F/3F/VFw0flv/W9RjnnUZqUjuOPyOsP29W+zNvCuL51BEWibePA5PNq9hjDVYHom/bmTv3LNExp8+nn/s949QuXc/zxLxdzCyMrK4qOdFgfJCuAUBweM33vWP63RcmPs12nX8v1Pk9UUklC0gFdxZ1U6JKEpF4f/nTESJeDPbvbGk8pKRllGm3uR9R90XtxUUZIn4e8PxzMmIlZjQG9uIVCIt6rVg35bF4dg9WvVgz2Z7hlymke5bzwLxwms9hVDRlkiapIW9C+8c7/5+V2et9Frcd/R95N2SF+bm8vArrX1b7hu6RjSZouFPI5OZlhn6+wz6m/B3HPq2sWOOpQUfVBaqRBSFxJSIF01UWhqMyuKmQ27iq4uKJ59+cOYHXN336sC6IUskPdgSCWocS8M//6Nl/ZZASSUCxZPzHj7m4ZD7youGi2xwPeWSl58HFDegZVEi/kY30m3kHxMJGjvx3FZ+d1aapJEmaVHHCr3r3HbobUy5YErYuZHXj4XfZVUrvVZIOUVaIn5EhEf7P8pPQ3+KOcO/MlEloigQNR1GLK7a/yrMnSZwcmMyOLHzifz3uODMvV6DFGaJ+Fw9dTPKtu55JJ77Jyh9zqP9H+WHS37g/w78v1DZS4NeYtYVs6hfqz6NazcOBZ147qItBdYSKe+YyMl7nhz1mN+C8Mq9cZ+yrBKY5prR7MbZNKrdKDDgIB75/bm/MtMzo7ryhHB3VlZGFj1b9yRZqBJRajR/y/4bAH3a9EmyJJVLaWMi9x55L2ftHT3Q8caDihM/+udBeXgReEGWSK30Wuy3635hZXUy64SiBXNuyGHJsCUAnNr1VE7d69TQ3CDPFTZs/2Exni4c/3Pdf/T9vDckOBlikCXihdSWZYEn7zqx1hApsxJJy4xpiQQpqmShSkSp0Xx01kfkDs9NWvK6qiLIneV/5ub1mjP2FJuyJWjipd9S+/LCL0tEdnmTIhNZ0S8jLSNsYHv86eNDs8Jb1m+JudNw5t5nljgv0srw8Pfc09PSQws8xaoX2cjXyahDh8Yd4pLfu06s9O/xjHX5lYiIFFsiQWMiFEdnJZtqFeKrKBVNImMB1RGvkfT3sIN6xxtu2kDdzLrUuje8J+5/T83qNmPiORNDkx0bZjW0WQO+vi8sUWFFEmQZBA1gQ8lxkGhWQJAlcufhd5JfmM+5+57LkO5D4gq59iyFWAq0rJZIYVFhcYRaQGRaKMQ3MIlH1aKWiKLUACJDZqG48fO7SxrVbhRolQUNFntldxx2R+i6ia4tXhpBLh1vQmIk/rTtEL0B779H/9C2J3/Tuk0ZdeIo6mbWpVHtRrRr1C7wXD8V7c5qWqcp2Y2zw9xZ0y6dRpemNodeKlgfflSJKEoNIBTimx4eBPBY/8eYefnMUs8PCh7wwnMz0jJCPeLKUiJBRMvuEDkoHs1V2adNH4b2skvrlmeOxWG72SUE/KHMkfNT4orOcu6wWw69pYQ7q3eb3mG59tSdpShKleL1ciNT8Xjpd6LhZYYOcvvVq1WPnC05ZKRlsH/b/eneojv3HRWcPbgyCFIiQQlIY7mFPPdbeZTI4K6DWXntSlo3KM4DFpktuSyWiKeAvLVlvAXM/JFv6s5SFKVK8Xz7QbmeYuG5kYIsEW/eREZaBvVr1WfWFbNKRGFVJv5MuwA3HXwTf1z7R4l6kbPR/XiWU3lne/sVCJR8X2WZJxI5kL61IHzhO3+IbyqgSkRRagDeSo6RlkhpeD3eoDERL9KrqiLbPjjzg7D9yPGKlvVaBiZY9Hr4QUokWk6s8pKIEilL+hJ/7qxko0pEUWoAniVS2nozkXiWSJA7yxt7qKqcTSd2Dl/bPHIAPdoEQS8dyAP9Hoh67Yp+hsj3VRYlUpY8YamAKhFFqQF4SqTMlohzmwSF2HqWSFUm/ht9YvEiUJH5vqJNEKyTWSe0wFkk3phIRTfc5XFnRavrD5+udu4sETlERC50283deh6KolQTvAiibi26lVLT8ucNf7LqulUhSyRorYqqtkQALu19aWg7Mo18WWaZe3gNc0W7hSLdfxXhzvJcb16W5lShVCUiIncCNwHDXVEm8EplCqUoSsVyzQHX8Me1f8Sdtr5p3aa0qt8q1FgFNWxebztZ7pc0SQtbajiRRZm8gfWK7tknYoncefid9N21b9iqpdGobpbIycBJQB6AMWYlUDbHqqIoSSVN0uJK9x50HgQ3gp47K9Yku8rmmgOuCW0nYhH5e/cVSSJKpHPTznx/yfdxZZSuVpYIkG/smzYAIhKca0BRlJ0Or8cb1Ah67qPIZXOTRSIr+4XcWRXcs/eWvfaoSJdfKlkhEJ8SeUNEngYai8ilwKfAM5UrlqIoqUAsd5ZnicRaNrcqScStVlmWyO2H3c73l3wf2q8IJeKlaTm+0/EppUhKfTJjzH9EpB+wCegC3GGMmVTpkimKknRiWSLewHpVWyLzrpwXuMpiKlki6Wnp9N21b2i/IpTIfrvuh7nTyjt56WQgeP2WqiauJ3NKQxWHotQw4hkTqWpLZM9me7Jnsz1LlJfHEom1emBFUNHBB9XKEhGRXAgFKNfCRmflGWPKFnCuKEq1w2tcg9w9Nx1yEwvXLeTCHhdWtViBlMsSqeSB6soKg06FAfZ43FlhkVgiMgjoG1xbUZSdCa+RCnKbtKrfig/P+rCqRYpKucZEKrlnn4gS6dC4A0s2LAk8Fut3qWrKbMMZY94Fjqx4URRFSTW8rLzxhJ0mm1S2RBKRbfHVi6Meq27urFN8u2lAH6ik5csURUkpLu51MRf3ujjZYsRFKlsiiYy5xFJsqeDG8ojHxhrg2y4AlgIDK0UaRVGUBEllS6SiqVaWiDEmNUbNFEVJOqnUeEWSypbIzkxUJSIijxPDbWWMubpSJFIUJSXZdPOmlO6xJ2KJeFmNgxbdqgjmXTmP6SunV/h1U+l3iGWJTKsyKRRFSXmCFnxKJRKxRB459hG6NO3CcZ2OqwSJos9pKS+e5WRSYHg6qhIxxrxYlYIoiqKUh0QskUa1G3HTITdVgjSVS3WxRAC7fgg2FXxXIGTzGWM0zFdRlJShuq0IWB5SaQwnnrizscA8oANwNzY668dKlElRFKXMJGKJVAcSWSelKoknxLepMeY5ERlmjJkCTBGRKZUtmKIoSlmoyhUWq4rl1ywPXN++WrmzgB3ue5WInACsBNpWnkiKoihlZ2d0Z7Vr1C6wPJXcWfEokXtFpBFwHfA40BD4v0qVSlEUpYzsrO6sIFIpd1Y8SuR7Y8xGYCPwt0qWR1EUJSF2RkskGqlkicQzsP6NiHwiIheLSJNKl0hRFCUBapIl4pEKYyOlKhFjTCfgNqAbMF1EPhSRcypdMkVRlDJQoyyRFHJnxZVa0hjzgzHmWuw6IusAnYioKEpKUZMskWrlzhKRhiJyvoj8D/gGWEU5F6USkQdFZL6IzBSRd0Skse/YcBFZJCILRORYX3lvEZnljj0mqWDHKYqSMtRESyQViMcS+QXoAdxjjOlsjLnJGFPejGKTgO7GmH2AX4HhACLSFRiCdZ31B54SCf1ljASGAp3cp385ZVAUZSeiJlkiqUQ80VkdTQU73owxn/h2vwMGu+2BwDhjzHZgiYgsAvqKyFKgoTHmWwAReQkYBPyvIuVSFKX6UqMskerkzqpoBRLARRQrg12B333HVriyXd12ZHkgIjJURKaJyLScnJwKFldRlFSkJlkiqeTOqrQ8ASLyKdAq4NCtxpj3XJ1bsasljvVOC6hvYpQHYowZDYwG6NOnT/LDFxRFqXRqoiWS0qngYyEitYwx+bHqGGOOLuUa5wMnAkf5rJ0VgH+ef1tsmpUVhKda8coVRVGAxNYxr66kkiUST3TWFyKS7dvvSzmz+IpIf2x6+ZOMMVt8h94HhohIloh0wA6g/2CMWQXkisgBLirrPOC98sigKMrORSo1rFVFKoyNxGOJ/BuYICKPYcchjgPKu+76E0AWMMn98N8ZYy43xswRkTeAuVg315XGmEJ3zhXAGKAOdgxFB9UVRamRpILy8ChViRhjJorI5diw3D+BnsaY1eW5qTFmjxjHRgAjAsqnAd3Lc19FUZSdgdCM9RQYE4nHnXU7NnvvYcBdwBcuJbyiKIqSBKqVJQI0A/oaY7YC34rIBOBZ4KNKlUxRFEUJJJXGf+KZJzIMQES6uP1lxph+lS2YoiiKkvrE484aAMwAJrj9HiLyfiXLpSiKokQhldxZ8QRW34VNuLgBwBgzA+hQaRIpiqIoMUkld1Y8YyIFxpiNEUInPyRAURQFmHbpNBb8tSDZYlQpoRnrKbCeSDxKZLaInAWki0gn4GpsSnhFUZSk07tNb3q36Z1sMaqUVLJE4nFnXYVNzb4deA3YBFxTiTIpiqIocZAKyiSeyYZbgFvdR1EURUky1cKdJSIfEDtT7kmVIpGiKIoSk1SwQDxiWSL/cd+nYFO6v+L2zwSWVqJMiqIoSgxSKcQ3qhIxxkwBEJF/GmMO8x36QES+rHTJFEVRlEBSyRKJZ2C9uYh09HZcivbmlSeSoiiKUl2IJ8T3/7BJF39z+9nAZZUmkaIoihKTauHO8jDGTHDzQ/Z0RfONMdsrVyxFURQlGqmUCj7e5XF7Yy2QDGBfEcEY81KlSaUoiqJEpVpZIiLyMrA7Ngmjt8qgAVSJKIqiJJFUUCbxWCJ9gK4mFWa1KIqiKCnlzoonOms2dp6IoiiKkgKkggXiEe/KhnNF5Ads/ixAZ6wriqIki1SaJxKPErmrsoVQFEVR4qdaWSLezHVFURRFiSRWAsavjDGHiEgu4YkYBTDGmIaVLp2iKIpSgmrhzjLGHOK+G1SdOIqiKEpppFIq+HiisxRFUZQUIpUsEVUiiqIo1YxUGlhXJaIoilJNSQWLRJWIoihKNSM0Y13HRBRFUZSyou4sRVEUJWFSwY3loUpEURSlmqGWiKIoirJToEpEURSlmqHuLEVRFCVhQjPWq8l6IoqiKEoKoZaIoiiKUm5SYYBdlYiiKEo1Q91ZDhG5XkSMiDTzlQ0XkUUiskBEjvWV9xaRWe7YY5JK9pyiKEoVkkrNX9KUiIi0A/oBy31lXYEhQDegP/CUiKS7wyOBoUAn9+lfpQIriqKkCKngxvJIpiXyCHAj4QteDQTGGWO2G2OWAIuAviLSGmhojPnW2GQxLwGDqlpgRVGUVKDGWyIichLwhzHml4hDuwK/+/ZXuLJd3XZkebTrDxWRaSIyLScnp4KkVhRFUSIpdY31RBGRT4FWAYduBW4Bjgk6LaDMxCgPxBgzGhgN0KdPn+SPPCmKolQgqeTOqjQlYow5OqhcRPYGOgC/OJOsLfCTiPTFWhjtfNXbAitdeduAckVRlBpHjU4Fb4yZZYxpYYzJNsZkYxVEL2PMauB9YIiIZIlIB+wA+g/GmFVArogc4KKyzgPeq2rZFUVRUoEaYYkkgjFmjoi8AcwFCoArjTGF7vAVwBigDvA/91EURalxpNLAetKViLNG/PsjgBEB9aYB3atILEVRFCUOdMa6oihKNSOV3FmqRBRFUaoZqeTOUiWiKIpSzdDcWYqiKErCqCWiKIqilJtUGBtRJaIoilLNUHeWoiiKkjDqzlIURVESJhXcWB6qRBRFUZSEUSWiKIqiJIwqEUVRFCVhVIkoiqIoCaNKRFEURUkYVSKKoihKwqgSURRFURJGlYiiKEo1pUYuj6soiqKUD52xriiKoiRMKlggHqpEFEVRlIRRJaIoilLNUHeWoiiKslOgSkRRFKWaouuJKIqiKNUaVSKKoijVlFRYV0SViKIoSjVF3VmKoihKmUkFC8RDlYiiKIqSMKpEFEVRlIRRJaIoiqIkjCoRRVEUJWFUiSiKolRTUiERoyoRRVEUJWFUiSiKolRTUiERoyoRRVGUaoq6sxRFUZQykwoWiIcqEUVRFCVhVIkoiqIoCZM0JSIiV4nIAhGZIyIP+MqHi8gid+xYX3lvEZnljj0mqWTPKYqi1FAyknFTEfkbMBDYxxizXURauPKuwBCgG9AG+FREOhtjCoGRwFDgO+BjoD/wv2TIryiKoliSZYlcAdxnjNkOYIxZ68oHAuOMMduNMUuARUBfEWkNNDTGfGtsOMJLwKAkyK0oipIy1ORU8J2BQ0XkexGZIiL7ufJdgd999Va4sl3ddmR5ICIyVESmici0nJycChZdURQluaRSKvhKc2eJyKdAq4BDt7r7NgEOAPYD3hCRjhD4ZkyM8kCMMaOB0QB9+vRJvqpWFEWpQFLBAvGoNCVijDk62jERuQJ427mmfhCRIqAZ1sJo56vaFljpytsGlCuKotRYUsEiSZY7613gSAAR6QzUAv4E3geGiEiWiHQAOgE/GGNWAbkicoCLyjoPeC8pkiuKoqQIqWCRJCU6C3geeF5EZgP5wPnOKpkjIm8Ac4EC4EoXmQV2MH4MUAcblaWRWYqi1EhSwQLxSIoSMcbkA+dEOTYCGBFQPg3oXsmiKYqipDzpaekA1M6onWRJkmeJKIqiKAnSs1VP7jjsDob2HppsUVSJKIqiVDdEhLv/dneyxQA0d5aiKIpSDlSJKIqiKAmjSkRRFEVJGFUiiqIoSsKoElEURVESRpWIoiiKkjCqRBRFUZSEUSWiKIqiJIzYlFU7LyKSAyxL4NRm2KSQ1QmVuWpQmasGlblqiCbzbsaY5qWdvNMrkUQRkWnGmD7JlqMsqMxVg8pcNajMVUN5ZVZ3lqIoipIwqkQURVGUhFElEp3RyRYgAVTmqkFlrhpU5qqhXDLrmIiiKIqSMGqJKIqiKAmjSkRRFEVJGFUiAYhIfxFZICKLROTmZMvjISLPi8hatza9V7aLiEwSkYXuu4nv2HD3DAtE5NgkyNtORCaLyDwRmSMiw6qBzLVF5AcR+cXJfHeqy+yTI11EfhaRD6uDzCKyVERmicgMEZlWTWRuLCLjRWS++7s+MJVlFpEu7v16n00ick2FymyM0Y/vA6QDi4GOQC3gF6BrsuVysh0G9AJm+8oeAG522zcD97vtrk72LKCDe6b0Kpa3NdDLbTcAfnVypbLMAtR325nA98ABqSyzT/ZrgVeBD1P9b8PJsRRoFlGW6jK/CFzitmsBjVNdZp/s6cBqYLeKlDkpD5PKH+BAYKJvfzgwPNly+eTJJlyJLABau+3WwIIguYGJwIFJlv09oF91kRmoC/wE7J/qMgNtgc+AI31KJNVlDlIiKSsz0BBYggtIqg4yR8h5DPB1Rcus7qyS7Ar87ttf4cpSlZbGmFUA7ruFK0+p5xCRbKAntmef0jI7t9AMYC0wyRiT8jIDjwI3AkW+slSX2QCfiMh0ERnqylJZ5o5ADvCCcxs+KyL1SG2Z/QwBXnPbFSazKpGSSEBZdYyDTpnnEJH6wFvANcaYTbGqBpRVuczGmEJjTA9s776viHSPUT3pMovIicBaY8z0eE8JKEvG38bBxphewHHAlSJyWIy6qSBzBtadPNIY0xPIw7qCopEKMgMgIrWAk4A3S6saUBZTZlUiJVkBtPPttwVWJkmWeFgjIq0B3PdaV54SzyEimVgFMtYY87YrTmmZPYwxG4AvgP6ktswHAyeJyFJgHHCkiLxCasuMMWal+14LvAP0JbVlXgGscJYpwHisUkllmT2OA34yxqxx+xUmsyqRkvwIdBKRDk57DwHeT7JMsXgfON9tn48dd/DKh4hIloh0ADoBP1SlYCIiwHPAPGPMw75DqSxzcxFp7LbrAEcD81NZZmPMcGNMW2NMNvbv9XNjzDmpLLOI1BORBt421l8/O5VlNsasBn4XkS6u6ChgLikss48zKXZlQUXKnKxBnlT+AMdjI4kWA7cmWx6fXK8Bq4Ad2B7DxUBT7IDqQve9i6/+re4ZFgDHJUHeQ7Cm8Exghvscn+Iy7wP87GSeDdzhylNW5gj5j6B4YD1lZcaOL/ziPnO8/7NUltnJ0AOY5v4+3gWaVAOZ6wJ/AY18ZRUms6Y9URRFURJG3VmKoihKwqgSURRFURJGlYiiKIqSMKpEFEVRlIRRJaIoiqIkjCqRGopEyVQsIg+6DKUzReQdb86E7/h0EaklIiNE5HcR2RxxfDcR+cyd/4WItPUday8in7jsp3NdKhREZIyILPFlGu0RIG8PETk+gecMzEgqImeKzSA7U0QmiEgz37HWTs4eIvKt2Gy+M0XkDF+dDiLyvcuC+rqbU4SInO3qzhSRb0RkX985JbIwl/FZxL33X907vNqV3+B7d7NFpFBEdnHHhrmyOSJyTRnvN0ZEBicia0UiNutsXd/+x5F/l0oSSUbcsn6S+yFGpmLspK8Mt30/Lrun288G3nfbB2ATt22OuPabwPlu+0jgZd+xL4B+brs+UNdtjwEGlyLzBcATZXzOwIyk2PQVa3HJ/7AZTe/ynXchcB3QGejkytpg5+g0dvtvAEPc9ijgCrd9ENDEbR8HfO+7bokszGV8nguBl4A0t98ioM4A7GRDgO7YuS513TN/6j1PnPcr9XdJ5G8vgXOWEpGoUT+p81FLpGbSF1hkjPnNGJOPTZUxEMAY84kxpsDV+w6b9sDjOGCCq/edcQncIuiKnbwEMNm7roh0xSqnSe78zcaYLfEI63r59wBnuN72GWLXQ3jX9fi/E5F9Ak4dCIwzxmw3xiwBFrlnF/ep52bVNyQ8tUN/4H/GmF+NMQudvCuxiqe5O+dIbNoLsOnBB7l63xhj1rvysPdnjPkSWBfPM0fhCuAeY0yRu97agDr+mcl7Ad8ZY7a433QKcHLkCRHW42ci0t53+GgRmeqsnxNd/W5i11yZ4c7p5MrP8ZU/LSLprnyziNwjIt8Dt4jIG757HyEiH7jtkSIyTcLXcbkaq8Ani8hkV7bUsxxF5Fpnac32LC0RyXaW2jPuWp+IzT6AiFztrOCZIjKu7D+BUoJkazH9VP0HGAw869s/l4BePvABcI5v/z2gY0SdSEvkVWCY2z4FO2O9KbaR/RB4Gzsj/EFcrxTb412AnQX8CJAVIMsFfhmBx4E73faRwIyAc56IkP85XM/avYNNWOviS58s6VGu1ReYh3UBN8MqYe9YOwKsC+B6/3t2ZdlBdeP83f7CziaeBvyPCKsCa3Gsw80+xiqRX937rwt8Czwe5Xc+321fBLzr+10muGfuhM2SUNu9+7NdnVpAHXevD4BMV/4UcJ7bNsDpbjsDWA7Uc/sjvd/IJ3c61mrdx+0vxWeJePtAb2AWUA9r2c7BZorOBgqAHq7+G757rPT+vnBWpX7K91FLpGZSaqZOEbkV+4841u3XAtoaY34r5drXA4eLyM/A4cAf7joZwKHu+H5YV9oF7pzhwJ6ufBfgpjie4RDgZQBjzOdAUxFpFFEn8DnFJoW8AtvgtMEqr+Hu+P7YdPXFF7EJ6l4GLjTWCojn/f0Nm5YmnmeJlyxgmzGmD/AM8HzE8QHY9SLWARhj5mFdkpOwyuAX7G8RyYFY5Q/2OQ/xHXvDGFNkrEX2G/Z3+hZrUdwE7GaM2YrNI9Ub+FFsGv2jsL8xQCE2CSfGWkQTgAEikgGcQHHeptNF5CdsJ6Mb1qqNxSHAO8aYPGPMZmwH5VB3bIkxZobbno5VLGB/67Eick6Ud6GUEVUiNZOYmTpF5HzgRGxv02scDwW+Ku3CxpiVxphTjE2Vfasr2+ju+bOxLrQCbN6hXu74KmPZDryA7fWXRjwpq6M9Zw9338Xu+d7AjmWAz2UHICINgY+A24wx37niP4HGrhH0X9c7Zx/gWWCgMeavOJ7FOy/dN0B+T0CVFbjGGJv1NtKF518vAveMzxljehljDsNaKQvjEMVE2XaXNK9i04pvBSaKyJHY3+NFY0wP9+lijLnLnbPNGFPou8brwOlYC/JHY0yu2GR/1wNHGWP2wb7z2qXIGfQ34LHdt12I7cSAVVpPYhXedN9vqCSIKpGaSdRMxSLSH9t7PsmEj1n0x7pQYiIizUTE+7saTnFv+UegiYg0d/tHYjOgej19L+vvIOxgcCS52CV2Pb4EznbnHQH8aUquVRItI+kfQFefLP2wriqwPejP3HVrYRvrl4wxoXUYnOKZjHWJgS8LqhtPeBs41xjza9A7ioZx65i4zx0BVd7FvjewVl7o+s4KO5ziXr1X3sIn1ylEKBnHN9i/AbDv1N9ZOE1E0kRkd6xlsUBEOgK/GWMew77jfbDvbLDvfruIyG5RHvULbAfiUqxCATsulQdsFJGWWGXuEfnbe3wJDBKRumIzAZ8MTI1yT9zfZTtjzGTsAl6NsW4wpTwk25+mn+R8iJKpGDv4/DvFWXdHufIfgTq+eg9ge8ZF7vsuVz4Y29v9Fdsbz/Kd0w/rTpiF9bfXcuWfu7LZwCu4Nc4j5N3FyTADOMPtv+eu9x3Ofx5wXmBGUuByrOKYifXlNwWa4yKbXJ1zsBmTZ/g+PdyxjliFtAgbkeb52Z8F1vvqT/Ndr0QW5jL+Zo2xPfRZWJfSvr5jF2CDCCLPmYpV1r9ge/lB1812v8FMrDJo78rHYMeoprrf80RXPhw7/jADa7V5YxlnuLKZWBfSAa58c8A9nwA24yL0fPeb557xbeACV34VNh3/ZLe/lOLIumvd381s7KJn3vP4l5C+HrgLyMQqSO9v7eZk/x/uDB/N4quUiti5Hs8YY44rtXI1xvnJ2xpj7ku2LIpSXVAloiiKoiSMjokoiqIoCaNKRFEURUkYVSKKoihKwqgSURRFURJGlYiiKIqSMKpEFEVRlIT5f22Unc5v+ZrHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(df2.SandP, color=\"green\")\n",
    "plt.xlabel(\"02/1965 to 08/2021 - 679 observations\")\n",
    "plt.ylabel(\"index value\")\n",
    "plt.title(\"S&P 500 after differencing\", weight = \"bold\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42200dcc",
   "metadata": {},
   "source": [
    "### Dickey Fuller test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "8ef77f72",
   "metadata": {},
   "outputs": [],
   "source": [
    "#now we'll apply ADF test on this data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 395,
   "id": "edce6e56",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value: 0.130492\n",
      "\n",
      "p-value: 0.000000\n",
      "\n",
      "p-value: 0.000000\n",
      "\n",
      "p-value: 0.000000\n",
      "\n",
      "p-value: 0.000000\n",
      "\n",
      "p-value: 0.000457\n",
      "\n",
      "p-value: 0.000000\n",
      "\n",
      "p-value: 0.000001\n",
      "\n",
      "p-value: 0.000033\n",
      "\n",
      "p-value: 0.000000\n"
     ]
    }
   ],
   "source": [
    "Z = df3[\"SandP\"]\n",
    "result = adfuller(Z)\n",
    "Z1 = df3[\"Industrial_Production_Index\"]\n",
    "result1 = adfuller(Z1)\n",
    "Z2 = df3[\"M1_money_supply\"]\n",
    "result2 = adfuller(Z2)\n",
    "Z3 = df3[\"three_Month_Tbill\"]\n",
    "result3 = adfuller(Z3)\n",
    "Z4 = df3[\"Moodys_AAA_rating\"]\n",
    "result4 = adfuller(Z4)\n",
    "Z5 = df3[\"CPI\"]\n",
    "result5 = adfuller(Z5)\n",
    "Z6 = df3[\"PPI\"]\n",
    "result6 = adfuller(Z6)\n",
    "Z7 = df3[\"three_month_CD_rate\"]\n",
    "result7 = adfuller(Z7)\n",
    "Z8 = df3[\"Consumer_credit_Owned_and_securitized\"]\n",
    "result8 = adfuller(Z8)\n",
    "Z9 = df3[\"Unemployment_rate\"]\n",
    "result9 = adfuller(Z9)\n",
    "print('p-value: %f' % result[1])\n",
    "print()\n",
    "print('p-value: %f' % result1[1])\n",
    "print()\n",
    "print('p-value: %f' % result2[1])\n",
    "print()\n",
    "print('p-value: %f' % result3[1])\n",
    "print()\n",
    "print('p-value: %f' % result4[1])\n",
    "print()\n",
    "print('p-value: %f' % result5[1])\n",
    "print()\n",
    "print('p-value: %f' % result6[1])\n",
    "print()\n",
    "print('p-value: %f' % result7[1])\n",
    "print()\n",
    "print('p-value: %f' % result8[1])\n",
    "print()\n",
    "print('p-value: %f' % result9[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "ae4cd9e5",
   "metadata": {},
   "outputs": [],
   "source": [
    "#since p value of SandP is more than 5 percent, we fail to reject the null and the data is non stationary for SandP\n",
    "#For independent variables, p value of all of them is coming out to be less than 5 percent, means they all are stationary \n",
    "#now compute second order differencing series for all dependent as well as independent variables"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3368fc56",
   "metadata": {},
   "source": [
    "### Second order differencing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 396,
   "id": "5afdc5bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SandP</th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>M1_money_supply</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>Moodys_AAA_rating</th>\n",
       "      <th>CPI</th>\n",
       "      <th>PPI</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Consumer_credit_Owned_and_securitized</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.55</td>\n",
       "      <td>0.216</td>\n",
       "      <td>0.4</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>3.000000e-02</td>\n",
       "      <td>0.03</td>\n",
       "      <td>-0.1</td>\n",
       "      <td>0.02</td>\n",
       "      <td>-0.205</td>\n",
       "      <td>-0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.06</td>\n",
       "      <td>-0.270</td>\n",
       "      <td>-0.1</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.1</td>\n",
       "      <td>-0.07</td>\n",
       "      <td>0.367</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.17</td>\n",
       "      <td>0.108</td>\n",
       "      <td>-0.8</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>8.881784e-16</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.03</td>\n",
       "      <td>-0.292</td>\n",
       "      <td>-0.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-5.55</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.8</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>1.000000e-02</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.2</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>0.105</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   SandP  Industrial_Production_Index  M1_money_supply  three_Month_Tbill  \\\n",
       "1    NaN                          NaN              NaN                NaN   \n",
       "2  -0.55                        0.216              0.4              -0.12   \n",
       "3   1.06                       -0.270             -0.1               0.00   \n",
       "4   0.17                        0.108             -0.8              -0.04   \n",
       "5  -5.55                        0.001              0.8              -0.05   \n",
       "\n",
       "   Moodys_AAA_rating   CPI  PPI  three_month_CD_rate  \\\n",
       "1                NaN   NaN  NaN                  NaN   \n",
       "2       3.000000e-02  0.03 -0.1                 0.02   \n",
       "3       0.000000e+00  0.04  0.1                -0.07   \n",
       "4       8.881784e-16  0.03  0.0                 0.03   \n",
       "5       1.000000e-02  0.03  0.2                -0.05   \n",
       "\n",
       "   Consumer_credit_Owned_and_securitized  Unemployment_rate  \n",
       "1                                    NaN                NaN  \n",
       "2                                 -0.205               -0.6  \n",
       "3                                  0.367                0.5  \n",
       "4                                 -0.292               -0.3  \n",
       "5                                  0.105                0.2  "
      ]
     },
     "execution_count": 396,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df4 = df3.diff()\n",
    "df4.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 397,
   "id": "10c5e571",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SandP</th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>M1_money_supply</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>Moodys_AAA_rating</th>\n",
       "      <th>CPI</th>\n",
       "      <th>PPI</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Consumer_credit_Owned_and_securitized</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.55</td>\n",
       "      <td>0.216</td>\n",
       "      <td>0.4</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>3.000000e-02</td>\n",
       "      <td>0.03</td>\n",
       "      <td>-0.1</td>\n",
       "      <td>0.02</td>\n",
       "      <td>-0.205</td>\n",
       "      <td>-0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.06</td>\n",
       "      <td>-0.270</td>\n",
       "      <td>-0.1</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.1</td>\n",
       "      <td>-0.07</td>\n",
       "      <td>0.367</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.17</td>\n",
       "      <td>0.108</td>\n",
       "      <td>-0.8</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>8.881784e-16</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.03</td>\n",
       "      <td>-0.292</td>\n",
       "      <td>-0.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-5.55</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.8</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>1.000000e-02</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.2</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>0.105</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>4.11</td>\n",
       "      <td>0.053</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.13</td>\n",
       "      <td>8.881784e-16</td>\n",
       "      <td>-0.16</td>\n",
       "      <td>-0.3</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>-0.079</td>\n",
       "      <td>-0.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   SandP  Industrial_Production_Index  M1_money_supply  three_Month_Tbill  \\\n",
       "2  -0.55                        0.216              0.4              -0.12   \n",
       "3   1.06                       -0.270             -0.1               0.00   \n",
       "4   0.17                        0.108             -0.8              -0.04   \n",
       "5  -5.55                        0.001              0.8              -0.05   \n",
       "6   4.11                        0.053              0.3               0.13   \n",
       "\n",
       "   Moodys_AAA_rating   CPI  PPI  three_month_CD_rate  \\\n",
       "2       3.000000e-02  0.03 -0.1                 0.02   \n",
       "3       0.000000e+00  0.04  0.1                -0.07   \n",
       "4       8.881784e-16  0.03  0.0                 0.03   \n",
       "5       1.000000e-02  0.03  0.2                -0.05   \n",
       "6       8.881784e-16 -0.16 -0.3                -0.01   \n",
       "\n",
       "   Consumer_credit_Owned_and_securitized  Unemployment_rate  \n",
       "2                                 -0.205               -0.6  \n",
       "3                                  0.367                0.5  \n",
       "4                                 -0.292               -0.3  \n",
       "5                                  0.105                0.2  \n",
       "6                                 -0.079               -0.2  "
      ]
     },
     "execution_count": 397,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df5 = df4.iloc[1: , :]\n",
    "df5.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 398,
   "id": "b662f493",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SandP</th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>M1_money_supply</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>Moodys_AAA_rating</th>\n",
       "      <th>CPI</th>\n",
       "      <th>PPI</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Consumer_credit_Owned_and_securitized</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.55</td>\n",
       "      <td>0.216</td>\n",
       "      <td>0.4</td>\n",
       "      <td>-1.200000e-01</td>\n",
       "      <td>3.000000e-02</td>\n",
       "      <td>0.030</td>\n",
       "      <td>-0.1</td>\n",
       "      <td>2.000000e-02</td>\n",
       "      <td>-0.205</td>\n",
       "      <td>-0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.06</td>\n",
       "      <td>-0.270</td>\n",
       "      <td>-0.1</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.040</td>\n",
       "      <td>0.1</td>\n",
       "      <td>-7.000000e-02</td>\n",
       "      <td>0.367</td>\n",
       "      <td>0.5</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.17</td>\n",
       "      <td>0.108</td>\n",
       "      <td>-0.8</td>\n",
       "      <td>-4.000000e-02</td>\n",
       "      <td>8.881784e-16</td>\n",
       "      <td>0.030</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.000000e-02</td>\n",
       "      <td>-0.292</td>\n",
       "      <td>-0.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-5.55</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.8</td>\n",
       "      <td>-5.000000e-02</td>\n",
       "      <td>1.000000e-02</td>\n",
       "      <td>0.030</td>\n",
       "      <td>0.2</td>\n",
       "      <td>-5.000000e-02</td>\n",
       "      <td>0.105</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.11</td>\n",
       "      <td>0.053</td>\n",
       "      <td>0.3</td>\n",
       "      <td>1.300000e-01</td>\n",
       "      <td>8.881784e-16</td>\n",
       "      <td>-0.160</td>\n",
       "      <td>-0.3</td>\n",
       "      <td>-1.000000e-02</td>\n",
       "      <td>-0.079</td>\n",
       "      <td>-0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>673</th>\n",
       "      <td>203.59</td>\n",
       "      <td>-2.697</td>\n",
       "      <td>-33.7</td>\n",
       "      <td>3.469447e-18</td>\n",
       "      <td>-4.800000e-01</td>\n",
       "      <td>0.407</td>\n",
       "      <td>-1.5</td>\n",
       "      <td>2.000000e-02</td>\n",
       "      <td>-0.672</td>\n",
       "      <td>0.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>674</th>\n",
       "      <td>-204.00</td>\n",
       "      <td>0.552</td>\n",
       "      <td>30.9</td>\n",
       "      <td>1.000000e-02</td>\n",
       "      <td>2.000000e-01</td>\n",
       "      <td>-0.320</td>\n",
       "      <td>4.1</td>\n",
       "      <td>-2.000000e-02</td>\n",
       "      <td>16.671</td>\n",
       "      <td>-0.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>675</th>\n",
       "      <td>43.97</td>\n",
       "      <td>-0.130</td>\n",
       "      <td>-231.9</td>\n",
       "      <td>2.000000e-02</td>\n",
       "      <td>-2.300000e-01</td>\n",
       "      <td>0.711</td>\n",
       "      <td>-3.4</td>\n",
       "      <td>-1.387779e-17</td>\n",
       "      <td>2.802</td>\n",
       "      <td>0.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>676</th>\n",
       "      <td>54.58</td>\n",
       "      <td>0.357</td>\n",
       "      <td>118.2</td>\n",
       "      <td>-1.000000e-02</td>\n",
       "      <td>-5.000000e-02</td>\n",
       "      <td>-1.146</td>\n",
       "      <td>-0.9</td>\n",
       "      <td>2.000000e-02</td>\n",
       "      <td>-20.913</td>\n",
       "      <td>-0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>677</th>\n",
       "      <td>-34.72</td>\n",
       "      <td>-0.439</td>\n",
       "      <td>112.5</td>\n",
       "      <td>-1.000000e-02</td>\n",
       "      <td>2.000000e-01</td>\n",
       "      <td>-0.537</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>-1.000000e-02</td>\n",
       "      <td>-2.895</td>\n",
       "      <td>0.3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>678 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      SandP  Industrial_Production_Index  M1_money_supply  three_Month_Tbill  \\\n",
       "0     -0.55                        0.216              0.4      -1.200000e-01   \n",
       "1      1.06                       -0.270             -0.1       0.000000e+00   \n",
       "2      0.17                        0.108             -0.8      -4.000000e-02   \n",
       "3     -5.55                        0.001              0.8      -5.000000e-02   \n",
       "4      4.11                        0.053              0.3       1.300000e-01   \n",
       "..      ...                          ...              ...                ...   \n",
       "673  203.59                       -2.697            -33.7       3.469447e-18   \n",
       "674 -204.00                        0.552             30.9       1.000000e-02   \n",
       "675   43.97                       -0.130           -231.9       2.000000e-02   \n",
       "676   54.58                        0.357            118.2      -1.000000e-02   \n",
       "677  -34.72                       -0.439            112.5      -1.000000e-02   \n",
       "\n",
       "     Moodys_AAA_rating    CPI  PPI  three_month_CD_rate  \\\n",
       "0         3.000000e-02  0.030 -0.1         2.000000e-02   \n",
       "1         0.000000e+00  0.040  0.1        -7.000000e-02   \n",
       "2         8.881784e-16  0.030  0.0         3.000000e-02   \n",
       "3         1.000000e-02  0.030  0.2        -5.000000e-02   \n",
       "4         8.881784e-16 -0.160 -0.3        -1.000000e-02   \n",
       "..                 ...    ...  ...                  ...   \n",
       "673      -4.800000e-01  0.407 -1.5         2.000000e-02   \n",
       "674       2.000000e-01 -0.320  4.1        -2.000000e-02   \n",
       "675      -2.300000e-01  0.711 -3.4        -1.387779e-17   \n",
       "676      -5.000000e-02 -1.146 -0.9         2.000000e-02   \n",
       "677       2.000000e-01 -0.537 -1.0        -1.000000e-02   \n",
       "\n",
       "     Consumer_credit_Owned_and_securitized  Unemployment_rate  \n",
       "0                                   -0.205               -0.6  \n",
       "1                                    0.367                0.5  \n",
       "2                                   -0.292               -0.3  \n",
       "3                                    0.105                0.2  \n",
       "4                                   -0.079               -0.2  \n",
       "..                                     ...                ...  \n",
       "673                                 -0.672                0.3  \n",
       "674                                 16.671               -0.4  \n",
       "675                                  2.802                0.4  \n",
       "676                                -20.913               -0.6  \n",
       "677                                 -2.895                0.3  \n",
       "\n",
       "[678 rows x 10 columns]"
      ]
     },
     "execution_count": 398,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df6 = df5.reset_index(drop=True)\n",
    "df6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 399,
   "id": "4f71b205",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value: 0.000000\n"
     ]
    }
   ],
   "source": [
    "Z10 = df6[\"SandP\"]\n",
    "result10 = adfuller(Z10)\n",
    "print('p-value: %f' % result10[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "6a0e6a41",
   "metadata": {},
   "outputs": [],
   "source": [
    "#we have got the p value of SnadP less than 5 percent, means the data is stationary now"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 400,
   "id": "a4795e22",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'S&P with Outliers')"
      ]
     },
     "execution_count": 400,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df6.boxplot(column=['SandP'])\n",
    "plt.title(\"S&P with Outliers\", weight = \"bold\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "7fe0d9b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df6.boxplot(column=['M1_money_supply'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "419e964c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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YkOJFYGX1JYksrJ6eHrLZLKlUivr6elKpFNlslp6enrBLEwmklnd2bgYeO9+bZrYF2ALQ0tJCoVCoYdciF69YLDI+Pk6hUOD06dMUCgXGx8cpFov6PZVImDXIzew54JoZ3sq4+1cr52SAEvCl87Xj7g8BD8HZG4J004UsFslkkkQiQWdn5+QNQfl8nmQyqZuDJBJmDXJ333Ch983sD4DfBtZ7GLeJilQpk8mQTqcn58jz+TzpdFpTKxIZVU2tmNltnL24+R/d/UxtShJZWF1dXXzzm9/kQx/60OSj3u6++25d6JTIqHaOfDfQBDxrZgAvuvs9VVclsoByuRxPPfUUTz/99LRVKx/84AcV5hIJ2jRLYq+trY2NGzeyf/9+isUiyWRy8rUeMCGLyfk2zdJ+5BJ7x48fZ2hoiL17906OyDdv3szJkyfDLk0kEN2iL7HX2NhId3f3tHXk3d3dNDY2hl2aSCAakUvsjY6Osnv3bm688cbJVSu7d+9mdHQ07NJEAlGQS+y1trayceNGuru7J+fIN23axP79+8MuTSQQBbnEXiaTmXGvFa0jl6hQkEvsTSwxnDoi7+np0dJDiQwtPxSZQs/slMVMz+wUuQDtRy5RpqkViT3tRy5RpxG5xJ72I5eoU5BL7BWLRTo6OqYd6+jooFgshlSRyNwoyCX2kskkfX1904719fWRTCZDqkhkbhTkEnsT+5Hn83lKpdLkfuSZTCbs0kQC0cVOiT2tI5eo0zpykSm0jlwWM60jFxG5RCnIRUQirqogN7O/MLMjZvaSmR0ws3fWqjAREQmm2hH559z9V939vcCTwGerL0lEROaiqiB39zemvFwCLPyVUxGRmKt6+aGZ9QD/GTgFpC5w3hZgC0BLSwuFQqHarkVq7vTp0/rdlMiZdfmhmT0HXDPDWxl3/+qU8z4DNLv7n83WqZYfymKl5YeymJ1v+eGsI3J33xCwj78HngJmDXIREamdaletrJ7y8nbg+9WVIyIic1XtHPn9ZvZuoAycBO6pviQREZmLqoLc3e+oVSEiInJxdGeniEjEKchFRCJOQS4iEnEKchGRiFOQi4hEnIJcRCTiFOQiIhGnIBcRiTgFuYhIxCnIRUQiTkEuIhJxCnIRkYhTkIuIRJyCXEQk4hTkIiIRpyAXEYk4BbmISMQpyEVEIq4mQW5mnzIzN7Ora9GeiIgEV3WQm9m1wG8Ar1ZfjoiIzFUtRuR/CdwLeA3aEhGROaqv5sNmdjvwmrt/18xmO3cLsAWgpaWFQqFQTdci8+L06dP63ZTIMfcLD6TN7DngmhneygD/FbjF3U+Z2Q+Bdnf/6Wydtre3e39//0WUKzK/CoUCnZ2dYZchMiMzO+Tu7ecen3Vqxd03uHvbuV/AK8D1wHcrIb4SOGxmM4W+yKKWy+Voa2tj/fr1tLW1kcvlwi5JJLCLnlpx9+8B75h4PZcRuchiksvlyGQyZLNZxsfHSSQSpNNpALq6ukKuTmR2WkcusdfT00M2myWVSlFfX08qlSKbzdLT0xN2aSKBVHWxcyp3X1WrtkQWUrFYpKOjY9qxjo4OisViSBWJzE3NglwkqpLJJPfddx/79++nWCySTCbZuHEjyWQy7NJEAlGQS+ylUil27tzJzp07aW1t5fjx42zfvp177rkn7NJEAlGQS+zl83m2b9/O3r17J0fk27dvZ//+/WGXJhLIrOvI54PWkctikkgkGB4epqGhYXId+djYGM3NzYyPj4ddnsiki15HLnKpSyaT9PX1TTvW19enOXKJDAW5xF4mkyGdTpPP5ymVSuTzedLpNJlMJuzSRALRHLnE3sRNP93d3ZNz5D09PboZSCJDc+QiU2ivFVnMNEcuInKJUpCLiEScglxEJOIU5CIiEacgFxGJuFBWrZjZvwMnF7xjkdldDWhPfVmsrnP3t597MJQgF1mszKx/puVdIouZplZERCJOQS4iEnEKcpHpHgq7AJG50hy5iEjEaUQuIhJxCnIRkYhTkIuIRJyCXOaVmb3NzP6o8nOnmT25gH1/0czOmNmVU471mpmb2dUX2ebHzeydU17/MEhbZvYJM3up8jVqZt+r/Hy/mf25mX1qhs+808y+XPl58u+uUsPui6lfLk0KcplvbwP+aC4fMLNEDft/Gfhwpd06IAW8VkV7HwfeOdtJ53L3v3P397r7e4EfA6nK6x0X+MyP3f3Oi65UYkNBLvPtfuCXzOwl4HPAFWb2ZTP7vpl9ycwMJke2nzWzPuD3zOwWM3vBzA6b2f80sysq573fzP7RzA6Z2TNmtnyW/nPARyo/dwIHgdLEm2a21cyOVr4+WTm2ysyKZvawmR0zswNmdpmZ3Qm0A1+qjKYvqzTTXanze2b2Kxf59/QeM/u6mf2Lmd09pY6jF9mexIiCXObbDuD/VEainwZuBD4JtAK/CKybcu6wu3cAzwF/Cmxw9/cB/cBWM2sAHgTudPf3A3uBnln6/xfg7Wa2FOgCHp14w8zeD3wC+DXgJuBuM7ux8vZq4AvufgPwOnCHu3+5UstHK6Pptyrn/rRS518DPzdFEtCvAr8F3Ax8dur0jchs9MxOWWjfcvcBgMoofRUw8Qj7xyrfb+Js0B+sDNgbgReAdwNtwLOV4wngXwP0+RXg9zkb2H845XgHsM/dhyr1fAX4D8ATwAl3f6ly3qFKnRdqf+K83w1Qz0y+WvmH4S0zywMfAF668EdEzlKQy0IbmfLzONN/B4cq3w141t2nPf3YzNYCx9z95jn2+ShwGHjE3cuVfwQm+gla52XnO3HKuef+eebi3DvzdKeeBKapFZlvbwJXznrWdC8C68zslwHM7HIzWwP8M2enSW6uHG8wsxtma8zdXwUywF+d89Y3gI2V9pcAvwP871mau5g/TxAfNrNmM/sFzs7lf3se+pBLlEbkMq/c/f+a2cHKRbu3gH8L8Jl/N7OPAzkza6oc/lN3/0HlguN/N7OrOPv7+9+AYwHa/JsZjh02sy8C36oc+lt3/46ZrbpAU18E9pjZW5ydz66VbwFPAe8C/sLdfzxLHSKTtNeKiEjEaWpFRCTiNLUikWdmX2D6MkaAXnf/u5Dq+QTwJ+ccPuju/yWMeuTSp6kVEZGI09SKiEjEKchFRCJOQS4iEnEKchGRiPt//wXgotW2YKIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df6.boxplot(column=['three_Month_Tbill'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "99796eee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df6.boxplot(column=['Moodys_AAA_rating'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "56c216ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df6.boxplot(column=['Consumer_credit_Owned_and_securitized'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "e3ef7ed6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df6.boxplot(column=['CPI'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "3991b2ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df6.boxplot(column=['PPI'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "f4354228",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df6.boxplot(column=['three_month_CD_rate'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "16ff6b06",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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9Tt35j9dI+iVJE22OjRWKkMfR8IJmZsD11kj6Ufb8pexxWq98Ji1pc0TsqD/Idn/d/pJ0sO71Qc39TM//x2X+azeoNSLiadvP236vpHfrlVl9fa3149aPPS3pnohY6Ju+G/2srdpf9/waSaMRcWG25FNb4BhL+nBEPNbmWEgEyzXIXURMSXrW9nppZi1c0vmSxpoctkPSJtvHZMecfgTLDBdla+pvkfTLkuYH3U5lAZ7947E3Iv4723ajZpZtbq2bPbfifkm/bvtXsn5/0fbphznmRUnHtTGGNDOT/0n2/Peb9LVD0mZn/62w/c42x8EKR8jjaPmYpM/aflDSiKSrIuKHTfa/UdKjkr6XXX55g9qf+T4m6VuS/k3SJyPif+dtv1JSyfZDkq6VdFndtjslvU5zl2oOKyJ+qpnQrWb93q9Dl4nm2y7pwmYnXhv4gqS/tP0dSR117aOSzpg98aqZGf8xkh7K3sdrWv9pkALuXYMkZVe73BUR/3yEx5c0czK01dAFliXW5IF5bF8haZPmrsUDKxIzeWAZsV2WdNG85tsiolJEPVj5CHkASBgnXgEgYYQ8ACSMkAeAhBHyAJCw/we8Vi/T2XdLKwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df6.boxplot(column=['Unemployment_rate'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "766fd1d2",
   "metadata": {},
   "source": [
    "### Remove outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "6390ab24",
   "metadata": {},
   "outputs": [],
   "source": [
    "Dates = df.Dates\n",
    "SandP = df.SandP\n",
    "IPI = df.Industrial_Production_Index\n",
    "M1 = df.M1_money_supply\n",
    "Tbill = df.three_Month_Tbill\n",
    "AAA = df.Moodys_AAA_rating\n",
    "CPI = df.CPI\n",
    "PPI = df.PPI\n",
    "CDrate = df.three_month_CD_rate\n",
    "Credit = df.Consumer_credit_Owned_and_securitized\n",
    "Unemp = df.Unemployment_rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 401,
   "id": "fb69e60a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "661\n",
      "\n",
      "662\n",
      "\n",
      "662\n",
      "\n",
      "663\n",
      "\n",
      "661\n",
      "\n",
      "660\n"
     ]
    }
   ],
   "source": [
    "print(df6.Unemployment_rate.idxmax())\n",
    "print()\n",
    "print(df6.Unemployment_rate.idxmin())\n",
    "print()\n",
    "print(df6.M1_money_supply.idxmax())\n",
    "print()\n",
    "print(df6.M1_money_supply.idxmin())\n",
    "print()\n",
    "print(df6.SandP.idxmax())\n",
    "print()\n",
    "print(df6.SandP.idxmin())\n",
    "#https://www.geeksforgeeks.org/find-maximum-values-position-in-columns-and-rows-of-a-dataframe-in-pandas/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 402,
   "id": "f43ff8fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SandP</th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>M1_money_supply</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>Moodys_AAA_rating</th>\n",
       "      <th>CPI</th>\n",
       "      <th>PPI</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Consumer_credit_Owned_and_securitized</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.55</td>\n",
       "      <td>0.216</td>\n",
       "      <td>0.4</td>\n",
       "      <td>-1.200000e-01</td>\n",
       "      <td>3.000000e-02</td>\n",
       "      <td>0.030</td>\n",
       "      <td>-0.1</td>\n",
       "      <td>2.000000e-02</td>\n",
       "      <td>-0.205</td>\n",
       "      <td>-0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.06</td>\n",
       "      <td>-0.270</td>\n",
       "      <td>-0.1</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.040</td>\n",
       "      <td>0.1</td>\n",
       "      <td>-7.000000e-02</td>\n",
       "      <td>0.367</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.17</td>\n",
       "      <td>0.108</td>\n",
       "      <td>-0.8</td>\n",
       "      <td>-4.000000e-02</td>\n",
       "      <td>8.881784e-16</td>\n",
       "      <td>0.030</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.000000e-02</td>\n",
       "      <td>-0.292</td>\n",
       "      <td>-0.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-5.55</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.8</td>\n",
       "      <td>-5.000000e-02</td>\n",
       "      <td>1.000000e-02</td>\n",
       "      <td>0.030</td>\n",
       "      <td>0.2</td>\n",
       "      <td>-5.000000e-02</td>\n",
       "      <td>0.105</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.11</td>\n",
       "      <td>0.053</td>\n",
       "      <td>0.3</td>\n",
       "      <td>1.300000e-01</td>\n",
       "      <td>8.881784e-16</td>\n",
       "      <td>-0.160</td>\n",
       "      <td>-0.3</td>\n",
       "      <td>-1.000000e-02</td>\n",
       "      <td>-0.079</td>\n",
       "      <td>-0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>673</th>\n",
       "      <td>203.59</td>\n",
       "      <td>-2.697</td>\n",
       "      <td>-33.7</td>\n",
       "      <td>3.469447e-18</td>\n",
       "      <td>-4.800000e-01</td>\n",
       "      <td>0.407</td>\n",
       "      <td>-1.5</td>\n",
       "      <td>2.000000e-02</td>\n",
       "      <td>-0.672</td>\n",
       "      <td>0.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>674</th>\n",
       "      <td>-204.00</td>\n",
       "      <td>0.552</td>\n",
       "      <td>30.9</td>\n",
       "      <td>1.000000e-02</td>\n",
       "      <td>2.000000e-01</td>\n",
       "      <td>-0.320</td>\n",
       "      <td>4.1</td>\n",
       "      <td>-2.000000e-02</td>\n",
       "      <td>16.671</td>\n",
       "      <td>-0.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>675</th>\n",
       "      <td>43.97</td>\n",
       "      <td>-0.130</td>\n",
       "      <td>-231.9</td>\n",
       "      <td>2.000000e-02</td>\n",
       "      <td>-2.300000e-01</td>\n",
       "      <td>0.711</td>\n",
       "      <td>-3.4</td>\n",
       "      <td>-1.387779e-17</td>\n",
       "      <td>2.802</td>\n",
       "      <td>0.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>676</th>\n",
       "      <td>54.58</td>\n",
       "      <td>0.357</td>\n",
       "      <td>118.2</td>\n",
       "      <td>-1.000000e-02</td>\n",
       "      <td>-5.000000e-02</td>\n",
       "      <td>-1.146</td>\n",
       "      <td>-0.9</td>\n",
       "      <td>2.000000e-02</td>\n",
       "      <td>-20.913</td>\n",
       "      <td>-0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>677</th>\n",
       "      <td>-34.72</td>\n",
       "      <td>-0.439</td>\n",
       "      <td>112.5</td>\n",
       "      <td>-1.000000e-02</td>\n",
       "      <td>2.000000e-01</td>\n",
       "      <td>-0.537</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>-1.000000e-02</td>\n",
       "      <td>-2.895</td>\n",
       "      <td>0.3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>676 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      SandP  Industrial_Production_Index  M1_money_supply  three_Month_Tbill  \\\n",
       "0     -0.55                        0.216              0.4      -1.200000e-01   \n",
       "1      1.06                       -0.270             -0.1       0.000000e+00   \n",
       "2      0.17                        0.108             -0.8      -4.000000e-02   \n",
       "3     -5.55                        0.001              0.8      -5.000000e-02   \n",
       "4      4.11                        0.053              0.3       1.300000e-01   \n",
       "..      ...                          ...              ...                ...   \n",
       "673  203.59                       -2.697            -33.7       3.469447e-18   \n",
       "674 -204.00                        0.552             30.9       1.000000e-02   \n",
       "675   43.97                       -0.130           -231.9       2.000000e-02   \n",
       "676   54.58                        0.357            118.2      -1.000000e-02   \n",
       "677  -34.72                       -0.439            112.5      -1.000000e-02   \n",
       "\n",
       "     Moodys_AAA_rating    CPI  PPI  three_month_CD_rate  \\\n",
       "0         3.000000e-02  0.030 -0.1         2.000000e-02   \n",
       "1         0.000000e+00  0.040  0.1        -7.000000e-02   \n",
       "2         8.881784e-16  0.030  0.0         3.000000e-02   \n",
       "3         1.000000e-02  0.030  0.2        -5.000000e-02   \n",
       "4         8.881784e-16 -0.160 -0.3        -1.000000e-02   \n",
       "..                 ...    ...  ...                  ...   \n",
       "673      -4.800000e-01  0.407 -1.5         2.000000e-02   \n",
       "674       2.000000e-01 -0.320  4.1        -2.000000e-02   \n",
       "675      -2.300000e-01  0.711 -3.4        -1.387779e-17   \n",
       "676      -5.000000e-02 -1.146 -0.9         2.000000e-02   \n",
       "677       2.000000e-01 -0.537 -1.0        -1.000000e-02   \n",
       "\n",
       "     Consumer_credit_Owned_and_securitized  Unemployment_rate  \n",
       "0                                   -0.205               -0.6  \n",
       "1                                    0.367                0.5  \n",
       "2                                   -0.292               -0.3  \n",
       "3                                    0.105                0.2  \n",
       "4                                   -0.079               -0.2  \n",
       "..                                     ...                ...  \n",
       "673                                 -0.672                0.3  \n",
       "674                                 16.671               -0.4  \n",
       "675                                  2.802                0.4  \n",
       "676                                -20.913               -0.6  \n",
       "677                                 -2.895                0.3  \n",
       "\n",
       "[676 rows x 10 columns]"
      ]
     },
     "execution_count": 402,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_6 = df6.drop([660, 661])\n",
    "df_6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "da8da918",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'S&P without Outliers')"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_6.boxplot(column=['SandP'])\n",
    "plt.title(\"S&P without Outliers\", weight = \"bold\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 403,
   "id": "fa985a96",
   "metadata": {},
   "outputs": [],
   "source": [
    "cols = df_6.columns\n",
    "#column names stored in cols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 405,
   "id": "a326da5a",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = cols[1:]\n",
    "y = cols[0:1]\n",
    "y = df_6[y]\n",
    "x = df_6[x]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 406,
   "id": "39b7a353",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>M1_money_supply</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>Moodys_AAA_rating</th>\n",
       "      <th>CPI</th>\n",
       "      <th>PPI</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Consumer_credit_Owned_and_securitized</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.216</td>\n",
       "      <td>0.4</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>3.000000e-02</td>\n",
       "      <td>0.03</td>\n",
       "      <td>-0.1</td>\n",
       "      <td>0.02</td>\n",
       "      <td>-0.205</td>\n",
       "      <td>-0.6</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.270</td>\n",
       "      <td>-0.1</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.1</td>\n",
       "      <td>-0.07</td>\n",
       "      <td>0.367</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.108</td>\n",
       "      <td>-0.8</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>8.881784e-16</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.03</td>\n",
       "      <td>-0.292</td>\n",
       "      <td>-0.3</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.001</td>\n",
       "      <td>0.8</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>1.000000e-02</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.2</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>0.105</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.053</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.13</td>\n",
       "      <td>8.881784e-16</td>\n",
       "      <td>-0.16</td>\n",
       "      <td>-0.3</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>-0.079</td>\n",
       "      <td>-0.2</td>\n",
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       "   Industrial_Production_Index  M1_money_supply  three_Month_Tbill  \\\n",
       "0                        0.216              0.4              -0.12   \n",
       "1                       -0.270             -0.1               0.00   \n",
       "2                        0.108             -0.8              -0.04   \n",
       "3                        0.001              0.8              -0.05   \n",
       "4                        0.053              0.3               0.13   \n",
       "\n",
       "   Moodys_AAA_rating   CPI  PPI  three_month_CD_rate  \\\n",
       "0       3.000000e-02  0.03 -0.1                 0.02   \n",
       "1       0.000000e+00  0.04  0.1                -0.07   \n",
       "2       8.881784e-16  0.03  0.0                 0.03   \n",
       "3       1.000000e-02  0.03  0.2                -0.05   \n",
       "4       8.881784e-16 -0.16 -0.3                -0.01   \n",
       "\n",
       "   Consumer_credit_Owned_and_securitized  Unemployment_rate  \n",
       "0                                 -0.205               -0.6  \n",
       "1                                  0.367                0.5  \n",
       "2                                 -0.292               -0.3  \n",
       "3                                  0.105                0.2  \n",
       "4                                 -0.079               -0.2  "
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     },
     "execution_count": 406,
     "metadata": {},
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  {
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   "execution_count": 42,
   "id": "29fb768f",
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   "outputs": [
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       "                                       Industrial_Production_Index  \\\n",
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       "three_Month_Tbill                                         0.022986   \n",
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       "CPI                                                       0.069882   \n",
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       "\n",
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       "      <td>0.602140</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.031752</td>\n",
       "      <td>0.146578</td>\n",
       "      <td>-0.269873</td>\n",
       "      <td>0.254137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <td>-0.054032</td>\n",
       "      <td>0.062251</td>\n",
       "      <td>-0.037780</td>\n",
       "      <td>0.807244</td>\n",
       "      <td>0.476227</td>\n",
       "      <td>0.034903</td>\n",
       "      <td>-0.031752</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.004423</td>\n",
       "      <td>-0.013996</td>\n",
       "      <td>-0.212853</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Consumer_credit_Owned_and_securitized</th>\n",
       "      <td>0.019217</td>\n",
       "      <td>0.153629</td>\n",
       "      <td>0.033358</td>\n",
       "      <td>0.013074</td>\n",
       "      <td>0.051654</td>\n",
       "      <td>0.159514</td>\n",
       "      <td>0.146578</td>\n",
       "      <td>0.004423</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.177631</td>\n",
       "      <td>0.075704</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Unemployment_rate</th>\n",
       "      <td>-0.080471</td>\n",
       "      <td>-0.608177</td>\n",
       "      <td>-0.584663</td>\n",
       "      <td>-0.025768</td>\n",
       "      <td>-0.116861</td>\n",
       "      <td>-0.129234</td>\n",
       "      <td>-0.269873</td>\n",
       "      <td>-0.013996</td>\n",
       "      <td>-0.177631</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.317004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fitted y</th>\n",
       "      <td>0.253848</td>\n",
       "      <td>-0.394581</td>\n",
       "      <td>0.036728</td>\n",
       "      <td>0.091629</td>\n",
       "      <td>-0.252985</td>\n",
       "      <td>0.245007</td>\n",
       "      <td>0.254137</td>\n",
       "      <td>-0.212853</td>\n",
       "      <td>0.075704</td>\n",
       "      <td>-0.317004</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                          SandP  Industrial_Production_Index  \\\n",
       "SandP                                  1.000000                    -0.100164   \n",
       "Industrial_Production_Index           -0.100164                     1.000000   \n",
       "M1_money_supply                        0.009323                     0.336271   \n",
       "three_Month_Tbill                      0.023260                     0.022986   \n",
       "Moodys_AAA_rating                     -0.064220                     0.103019   \n",
       "CPI                                    0.062195                     0.069882   \n",
       "PPI                                    0.064512                     0.098346   \n",
       "three_month_CD_rate                   -0.054032                     0.062251   \n",
       "Consumer_credit_Owned_and_securitized  0.019217                     0.153629   \n",
       "Unemployment_rate                     -0.080471                    -0.608177   \n",
       "fitted y                               0.253848                    -0.394581   \n",
       "\n",
       "                                       M1_money_supply  three_Month_Tbill  \\\n",
       "SandP                                         0.009323           0.023260   \n",
       "Industrial_Production_Index                   0.336271           0.022986   \n",
       "M1_money_supply                               1.000000           0.004929   \n",
       "three_Month_Tbill                             0.004929           1.000000   \n",
       "Moodys_AAA_rating                             0.079677           0.471266   \n",
       "CPI                                          -0.004707          -0.010322   \n",
       "PPI                                           0.208606          -0.006927   \n",
       "three_month_CD_rate                          -0.037780           0.807244   \n",
       "Consumer_credit_Owned_and_securitized         0.033358           0.013074   \n",
       "Unemployment_rate                            -0.584663          -0.025768   \n",
       "fitted y                                      0.036728           0.091629   \n",
       "\n",
       "                                       Moodys_AAA_rating       CPI       PPI  \\\n",
       "SandP                                          -0.064220  0.062195  0.064512   \n",
       "Industrial_Production_Index                     0.103019  0.069882  0.098346   \n",
       "M1_money_supply                                 0.079677 -0.004707  0.208606   \n",
       "three_Month_Tbill                               0.471266 -0.010322 -0.006927   \n",
       "Moodys_AAA_rating                               1.000000  0.058895  0.090063   \n",
       "CPI                                             0.058895  1.000000  0.602140   \n",
       "PPI                                             0.090063  0.602140  1.000000   \n",
       "three_month_CD_rate                             0.476227  0.034903 -0.031752   \n",
       "Consumer_credit_Owned_and_securitized           0.051654  0.159514  0.146578   \n",
       "Unemployment_rate                              -0.116861 -0.129234 -0.269873   \n",
       "fitted y                                       -0.252985  0.245007  0.254137   \n",
       "\n",
       "                                       three_month_CD_rate  \\\n",
       "SandP                                            -0.054032   \n",
       "Industrial_Production_Index                       0.062251   \n",
       "M1_money_supply                                  -0.037780   \n",
       "three_Month_Tbill                                 0.807244   \n",
       "Moodys_AAA_rating                                 0.476227   \n",
       "CPI                                               0.034903   \n",
       "PPI                                              -0.031752   \n",
       "three_month_CD_rate                               1.000000   \n",
       "Consumer_credit_Owned_and_securitized             0.004423   \n",
       "Unemployment_rate                                -0.013996   \n",
       "fitted y                                         -0.212853   \n",
       "\n",
       "                                       Consumer_credit_Owned_and_securitized  \\\n",
       "SandP                                                               0.019217   \n",
       "Industrial_Production_Index                                         0.153629   \n",
       "M1_money_supply                                                     0.033358   \n",
       "three_Month_Tbill                                                   0.013074   \n",
       "Moodys_AAA_rating                                                   0.051654   \n",
       "CPI                                                                 0.159514   \n",
       "PPI                                                                 0.146578   \n",
       "three_month_CD_rate                                                 0.004423   \n",
       "Consumer_credit_Owned_and_securitized                               1.000000   \n",
       "Unemployment_rate                                                  -0.177631   \n",
       "fitted y                                                            0.075704   \n",
       "\n",
       "                                       Unemployment_rate  fitted y  \n",
       "SandP                                          -0.080471  0.253848  \n",
       "Industrial_Production_Index                    -0.608177 -0.394581  \n",
       "M1_money_supply                                -0.584663  0.036728  \n",
       "three_Month_Tbill                              -0.025768  0.091629  \n",
       "Moodys_AAA_rating                              -0.116861 -0.252985  \n",
       "CPI                                            -0.129234  0.245007  \n",
       "PPI                                            -0.269873  0.254137  \n",
       "three_month_CD_rate                            -0.013996 -0.212853  \n",
       "Consumer_credit_Owned_and_securitized          -0.177631  0.075704  \n",
       "Unemployment_rate                               1.000000 -0.317004  \n",
       "fitted y                                       -0.317004  1.000000  "
      ]
     },
     "execution_count": 413,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_6.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16c5511b",
   "metadata": {},
   "source": [
    "### First Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "d81da435",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = ols('SandP ~ Industrial_Production_Index + M1_money_supply + three_Month_Tbill + Moodys_AAA_rating + CPI + PPI + three_month_CD_rate + Consumer_credit_Owned_and_securitized + Unemployment_rate',df_6).fit()\n",
    "#we'll write the equation that we want"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "id": "79429645",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>SandP</td>      <th>  R-squared:         </th> <td>   0.064</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.052</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   5.097</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sun, 31 Oct 2021</td> <th>  Prob (F-statistic):</th> <td>1.10e-06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>13:22:32</td>     <th>  Log-Likelihood:    </th> <td> -3510.7</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   676</td>      <th>  AIC:               </th> <td>   7041.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   666</td>      <th>  BIC:               </th> <td>   7087.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     9</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "                    <td></td>                       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>                             <td>   -0.1639</td> <td>    1.690</td> <td>   -0.097</td> <td> 0.923</td> <td>   -3.482</td> <td>    3.154</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Industrial_Production_Index</th>           <td>  -11.2568</td> <td>    2.425</td> <td>   -4.642</td> <td> 0.000</td> <td>  -16.018</td> <td>   -6.496</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>M1_money_supply</th>                       <td>   -0.0048</td> <td>    0.004</td> <td>   -1.350</td> <td> 0.177</td> <td>   -0.012</td> <td>    0.002</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>three_Month_Tbill</th>                     <td>   17.8090</td> <td>    5.867</td> <td>    3.035</td> <td> 0.002</td> <td>    6.289</td> <td>   29.329</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Moodys_AAA_rating</th>                     <td>  -13.9564</td> <td>    7.446</td> <td>   -1.874</td> <td> 0.061</td> <td>  -28.578</td> <td>    0.665</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>CPI</th>                                   <td>    5.7818</td> <td>    4.914</td> <td>    1.177</td> <td> 0.240</td> <td>   -3.868</td> <td>   15.431</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>PPI</th>                                   <td>    0.0142</td> <td>    1.524</td> <td>    0.009</td> <td> 0.993</td> <td>   -2.979</td> <td>    3.008</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>three_month_CD_rate</th>                   <td>  -12.2393</td> <td>    4.775</td> <td>   -2.563</td> <td> 0.011</td> <td>  -21.616</td> <td>   -2.863</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Consumer_credit_Owned_and_securitized</th> <td>    0.0158</td> <td>    0.150</td> <td>    0.105</td> <td> 0.916</td> <td>   -0.279</td> <td>    0.311</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Unemployment_rate</th>                     <td>  -21.9026</td> <td>    4.914</td> <td>   -4.457</td> <td> 0.000</td> <td>  -31.551</td> <td>  -12.254</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>87.292</td> <th>  Durbin-Watson:     </th> <td>   2.825</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td> 828.726</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.026</td> <th>  Prob(JB):          </th> <td>1.11e-180</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 8.424</td> <th>  Cond. No.          </th> <td>2.71e+03</td> \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 2.71e+03. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                  SandP   R-squared:                       0.064\n",
       "Model:                            OLS   Adj. R-squared:                  0.052\n",
       "Method:                 Least Squares   F-statistic:                     5.097\n",
       "Date:                Sun, 31 Oct 2021   Prob (F-statistic):           1.10e-06\n",
       "Time:                        13:22:32   Log-Likelihood:                -3510.7\n",
       "No. Observations:                 676   AIC:                             7041.\n",
       "Df Residuals:                     666   BIC:                             7087.\n",
       "Df Model:                           9                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "=========================================================================================================\n",
       "                                            coef    std err          t      P>|t|      [0.025      0.975]\n",
       "---------------------------------------------------------------------------------------------------------\n",
       "Intercept                                -0.1639      1.690     -0.097      0.923      -3.482       3.154\n",
       "Industrial_Production_Index             -11.2568      2.425     -4.642      0.000     -16.018      -6.496\n",
       "M1_money_supply                          -0.0048      0.004     -1.350      0.177      -0.012       0.002\n",
       "three_Month_Tbill                        17.8090      5.867      3.035      0.002       6.289      29.329\n",
       "Moodys_AAA_rating                       -13.9564      7.446     -1.874      0.061     -28.578       0.665\n",
       "CPI                                       5.7818      4.914      1.177      0.240      -3.868      15.431\n",
       "PPI                                       0.0142      1.524      0.009      0.993      -2.979       3.008\n",
       "three_month_CD_rate                     -12.2393      4.775     -2.563      0.011     -21.616      -2.863\n",
       "Consumer_credit_Owned_and_securitized     0.0158      0.150      0.105      0.916      -0.279       0.311\n",
       "Unemployment_rate                       -21.9026      4.914     -4.457      0.000     -31.551     -12.254\n",
       "==============================================================================\n",
       "Omnibus:                       87.292   Durbin-Watson:                   2.825\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              828.726\n",
       "Skew:                          -0.026   Prob(JB):                    1.11e-180\n",
       "Kurtosis:                       8.424   Cond. No.                     2.71e+03\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 2.71e+03. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "f95ccd3e",
   "metadata": {},
   "outputs": [],
   "source": [
    "#p value of the vatiables should be less that 5 percent and t stats should be greater than 1.96\n",
    "#r sq should be high\n",
    "#all the assumptions should be correct - multicollinearity, autocorrelation, linearity and hateroskedasticity\n",
    "#for multicillinearity we do not want VIF greater than 5\n",
    "#variance of error terms should be constant\n",
    "#linearity - reset test\n",
    "#model should be general enough to work on out of sample data - Generalization\n",
    "#autocorrelation means that y is dependent on its own past value\n",
    "#multicollinearity means any two independent variable are highly correlated\n",
    "#hateroskedascity - there should be a single constant variance in my model, means there should not be any correlation between error term and any independent vatriable. \n",
    "#if there is any correlation btw error and any independent variable, it means error is not purely random,  \n",
    "# and it means error includes some independent variable that is not included in the model \n",
    "#problem of Hateroskedasticity means variance of error terms is not constant \n",
    "\n",
    "#Stepwise regression: \n",
    "\n",
    "#    remove problem of multicollinearity - removing correlated independent variables\n",
    "#    variable selection - deciding important variables\n",
    "#    removing the problem of autocorrelation\n",
    "#    removing the problem of hateroskedcty\n",
    "#    checking the accuracy of model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 407,
   "id": "23e8f117",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept                                -0.163873\n",
       "Industrial_Production_Index             -11.256825\n",
       "M1_money_supply                          -0.004766\n",
       "three_Month_Tbill                        17.809003\n",
       "Moodys_AAA_rating                       -13.956366\n",
       "CPI                                       5.781805\n",
       "PPI                                       0.014192\n",
       "three_month_CD_rate                     -12.239290\n",
       "Consumer_credit_Owned_and_securitized     0.015771\n",
       "Unemployment_rate                       -21.902579\n",
       "dtype: float64"
      ]
     },
     "execution_count": 407,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coefficient = model.params\n",
    "coefficient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 408,
   "id": "7027dfbc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0644389788742672"
      ]
     },
     "execution_count": 408,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.rsquared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "4b0f5a0c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept                                0.922768\n",
       "Industrial_Production_Index              0.000004\n",
       "M1_money_supply                          0.177477\n",
       "three_Month_Tbill                        0.002496\n",
       "Moodys_AAA_rating                        0.061337\n",
       "CPI                                      0.239803\n",
       "PPI                                      0.992575\n",
       "three_month_CD_rate                      0.010594\n",
       "Consumer_credit_Owned_and_securitized    0.916467\n",
       "Unemployment_rate                        0.000010\n",
       "dtype: float64"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.pvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 409,
   "id": "a1a4af08",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0       7.912539\n",
       "1      -6.980113\n",
       "2       4.284286\n",
       "3      -4.799559\n",
       "4       5.125572\n",
       "         ...    \n",
       "673    32.561186\n",
       "674    -1.661329\n",
       "675     1.316550\n",
       "676     1.702103\n",
       "677    -8.340670\n",
       "Length: 676, dtype: float64"
      ]
     },
     "execution_count": 409,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "forecasted_y = model.fittedvalues\n",
    "forecasted_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 410,
   "id": "7e911b51",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SandP</th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>M1_money_supply</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>Moodys_AAA_rating</th>\n",
       "      <th>CPI</th>\n",
       "      <th>PPI</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Consumer_credit_Owned_and_securitized</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "      <th>fitted y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.55</td>\n",
       "      <td>0.216</td>\n",
       "      <td>0.4</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>3.000000e-02</td>\n",
       "      <td>0.03</td>\n",
       "      <td>-0.1</td>\n",
       "      <td>0.02</td>\n",
       "      <td>-0.205</td>\n",
       "      <td>-0.6</td>\n",
       "      <td>7.912539</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.06</td>\n",
       "      <td>-0.270</td>\n",
       "      <td>-0.1</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.1</td>\n",
       "      <td>-0.07</td>\n",
       "      <td>0.367</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-6.980113</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.17</td>\n",
       "      <td>0.108</td>\n",
       "      <td>-0.8</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>8.881784e-16</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.03</td>\n",
       "      <td>-0.292</td>\n",
       "      <td>-0.3</td>\n",
       "      <td>4.284286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-5.55</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.8</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>1.000000e-02</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.2</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>0.105</td>\n",
       "      <td>0.2</td>\n",
       "      <td>-4.799559</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.11</td>\n",
       "      <td>0.053</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.13</td>\n",
       "      <td>8.881784e-16</td>\n",
       "      <td>-0.16</td>\n",
       "      <td>-0.3</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>-0.079</td>\n",
       "      <td>-0.2</td>\n",
       "      <td>5.125572</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   SandP  Industrial_Production_Index  M1_money_supply  three_Month_Tbill  \\\n",
       "0  -0.55                        0.216              0.4              -0.12   \n",
       "1   1.06                       -0.270             -0.1               0.00   \n",
       "2   0.17                        0.108             -0.8              -0.04   \n",
       "3  -5.55                        0.001              0.8              -0.05   \n",
       "4   4.11                        0.053              0.3               0.13   \n",
       "\n",
       "   Moodys_AAA_rating   CPI  PPI  three_month_CD_rate  \\\n",
       "0       3.000000e-02  0.03 -0.1                 0.02   \n",
       "1       0.000000e+00  0.04  0.1                -0.07   \n",
       "2       8.881784e-16  0.03  0.0                 0.03   \n",
       "3       1.000000e-02  0.03  0.2                -0.05   \n",
       "4       8.881784e-16 -0.16 -0.3                -0.01   \n",
       "\n",
       "   Consumer_credit_Owned_and_securitized  Unemployment_rate  fitted y  \n",
       "0                                 -0.205               -0.6  7.912539  \n",
       "1                                  0.367                0.5 -6.980113  \n",
       "2                                 -0.292               -0.3  4.284286  \n",
       "3                                  0.105                0.2 -4.799559  \n",
       "4                                 -0.079               -0.2  5.125572  "
      ]
     },
     "execution_count": 410,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_6.loc[:,'fitted y'] = forecasted_y\n",
    "#adding predicted y in the last column of data\n",
    "df_6.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "3d07a699",
   "metadata": {},
   "outputs": [],
   "source": [
    "#for Multicollinearity - we compute variance inflation factor, problem of multicollin inflates variance of error terms, but we want it to be low\n",
    "#VIF above 5/10 is not acceptable\n",
    "#VIF = 1/(1-r sq)\n",
    "#for computing the VIF of all independent variables, we'll have to make them as dependent variavbles and run regression with other independent variables\n",
    "#Industrial_Production_index ~ M1 + threemonth + .......\n",
    "#then - M1_money_supply ~ Industrial_Production_index + three month + .......\n",
    "# so, 9 VIFs will be calculated\n",
    "#store all the VIFs in a table. Check maximum value of the table. \n",
    "#then delete the variable with VIF greater than 5\n",
    "#again calculate VIF for the remaining 8 variables..and so on and on\n",
    "\n",
    "\n",
    "#Then rerun the regression for all remaining independent variable by making them as dependent variable\n",
    "#again repeat the above steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "31c3aec8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pandas.core.indexes.base.Index"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(cols)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 411,
   "id": "6c97dc54",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-83.27170128882543"
      ]
     },
     "execution_count": 411,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.max()\n",
    "forecasted_y.max()\n",
    "y.min()\n",
    "forecasted_y.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 412,
   "id": "81fa4a2a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Actual vs Predicted S&P')"
      ]
     },
     "execution_count": 412,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(y,forecasted_y)\n",
    "plt.xlabel('Actual')\n",
    "plt.ylabel('Predicted')\n",
    "plt.title('Actual vs Predicted S&P')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "accf75ba",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "ebcb5941",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "#https://www.geeksforgeeks.org/find-maximum-values-position-in-columns-and-rows-of-a-dataframe-in-pandas/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "614593af",
   "metadata": {},
   "outputs": [],
   "source": [
    "#deleting extreme outliers only"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "84ab48c3",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "30f9af0f",
   "metadata": {},
   "outputs": [],
   "source": [
    "#plt.plot(df6[\"CPI\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "9a500aa4",
   "metadata": {},
   "outputs": [],
   "source": [
    "#SandP stationary after second order differencing\n",
    "#Industrial_Production_Index is stationary\n",
    "#M1_money_supply is stationary\n",
    "#three_Month_Tbill is stationary\n",
    "#Moodys_AAA_rating is stationary\n",
    "#CPI and PPI is stationary\n",
    "#three_month_CD_rate is stationary\n",
    "#Consumer_credit_Owned_and_securitized is stationary\n",
    "#Unemployment_rate is stationary\n",
    "\n",
    "# All indepoendent variavbles are stationary at first differencing only and only Dependent variable i.e. SandP is stationary\n",
    "#after second order differencing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "93f1d98e",
   "metadata": {},
   "outputs": [],
   "source": [
    "#For updating the master sheet - data = pd.concate([y,x],axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2ba3e6f2",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1e3ed29c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b2171b43",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3b8ff97d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "54397153",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "15fd5b70",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "adbc22a0",
   "metadata": {},
   "source": [
    "### Important Variable Selection using Backward selection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "a87ba6dc",
   "metadata": {},
   "outputs": [],
   "source": [
    "p_value = list(model.pvalues)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "id": "6d68043e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept                                0.922768\n",
       "Industrial_Production_Index              0.000004\n",
       "M1_money_supply                          0.177477\n",
       "three_Month_Tbill                        0.002496\n",
       "Moodys_AAA_rating                        0.061337\n",
       "CPI                                      0.239803\n",
       "PPI                                      0.992575\n",
       "three_month_CD_rate                      0.010594\n",
       "Consumer_credit_Owned_and_securitized    0.916467\n",
       "Unemployment_rate                        0.000010\n",
       "dtype: float64"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.pvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "715037ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.9227678446056008,\n",
       " 4.152640876141203e-06,\n",
       " 0.17747683683422943,\n",
       " 0.0024961179772333753,\n",
       " 0.061337221453206706,\n",
       " 0.23980256613695808,\n",
       " 0.9925747700033763,\n",
       " 0.010594271410012948,\n",
       " 0.9164671273115778,\n",
       " 9.735090132266551e-06]"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_value    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 414,
   "id": "3180bc53",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Drop the variable PPI\n"
     ]
    }
   ],
   "source": [
    "if max(p_value[1:]) > 0.05:\n",
    "    max_value = df_6.columns[p_value.index(max(p_value[1:]))]\n",
    "    print('Drop the variable ' + str(max_value))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 415,
   "id": "643fcb8c",
   "metadata": {},
   "outputs": [],
   "source": [
    "df7 = df_6.drop(columns=['PPI','fitted y'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 416,
   "id": "d63596b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SandP</th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>M1_money_supply</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>Moodys_AAA_rating</th>\n",
       "      <th>CPI</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Consumer_credit_Owned_and_securitized</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.55</td>\n",
       "      <td>0.216</td>\n",
       "      <td>0.4</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>3.000000e-02</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.02</td>\n",
       "      <td>-0.205</td>\n",
       "      <td>-0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.06</td>\n",
       "      <td>-0.270</td>\n",
       "      <td>-0.1</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.04</td>\n",
       "      <td>-0.07</td>\n",
       "      <td>0.367</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.17</td>\n",
       "      <td>0.108</td>\n",
       "      <td>-0.8</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>8.881784e-16</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.03</td>\n",
       "      <td>-0.292</td>\n",
       "      <td>-0.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-5.55</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.8</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>1.000000e-02</td>\n",
       "      <td>0.03</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>0.105</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.11</td>\n",
       "      <td>0.053</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.13</td>\n",
       "      <td>8.881784e-16</td>\n",
       "      <td>-0.16</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>-0.079</td>\n",
       "      <td>-0.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   SandP  Industrial_Production_Index  M1_money_supply  three_Month_Tbill  \\\n",
       "0  -0.55                        0.216              0.4              -0.12   \n",
       "1   1.06                       -0.270             -0.1               0.00   \n",
       "2   0.17                        0.108             -0.8              -0.04   \n",
       "3  -5.55                        0.001              0.8              -0.05   \n",
       "4   4.11                        0.053              0.3               0.13   \n",
       "\n",
       "   Moodys_AAA_rating   CPI  three_month_CD_rate  \\\n",
       "0       3.000000e-02  0.03                 0.02   \n",
       "1       0.000000e+00  0.04                -0.07   \n",
       "2       8.881784e-16  0.03                 0.03   \n",
       "3       1.000000e-02  0.03                -0.05   \n",
       "4       8.881784e-16 -0.16                -0.01   \n",
       "\n",
       "   Consumer_credit_Owned_and_securitized  Unemployment_rate  \n",
       "0                                 -0.205               -0.6  \n",
       "1                                  0.367                0.5  \n",
       "2                                 -0.292               -0.3  \n",
       "3                                  0.105                0.2  \n",
       "4                                 -0.079               -0.2  "
      ]
     },
     "execution_count": 416,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df7.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "id": "93f9e309",
   "metadata": {},
   "outputs": [],
   "source": [
    "model1 = ols('SandP ~ Industrial_Production_Index + M1_money_supply + three_Month_Tbill + Moodys_AAA_rating + CPI + three_month_CD_rate + Consumer_credit_Owned_and_securitized + Unemployment_rate',df7).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 417,
   "id": "c6302271",
   "metadata": {},
   "outputs": [],
   "source": [
    "forecasted_y1 = model1.fittedvalues\n",
    "df7.loc[:,'fitted y1'] = forecasted_y1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 418,
   "id": "eda03be5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SandP</th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>M1_money_supply</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>Moodys_AAA_rating</th>\n",
       "      <th>CPI</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Consumer_credit_Owned_and_securitized</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "      <th>fitted y1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.55</td>\n",
       "      <td>0.216</td>\n",
       "      <td>0.4</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>3.000000e-02</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.02</td>\n",
       "      <td>-0.205</td>\n",
       "      <td>-0.6</td>\n",
       "      <td>7.917657</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.06</td>\n",
       "      <td>-0.270</td>\n",
       "      <td>-0.1</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.04</td>\n",
       "      <td>-0.07</td>\n",
       "      <td>0.367</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-6.982639</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.17</td>\n",
       "      <td>0.108</td>\n",
       "      <td>-0.8</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>8.881784e-16</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.03</td>\n",
       "      <td>-0.292</td>\n",
       "      <td>-0.3</td>\n",
       "      <td>4.286416</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-5.55</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.8</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>1.000000e-02</td>\n",
       "      <td>0.03</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>0.105</td>\n",
       "      <td>0.2</td>\n",
       "      <td>-4.802702</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.11</td>\n",
       "      <td>0.053</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.13</td>\n",
       "      <td>8.881784e-16</td>\n",
       "      <td>-0.16</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>-0.079</td>\n",
       "      <td>-0.2</td>\n",
       "      <td>5.126947</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   SandP  Industrial_Production_Index  M1_money_supply  three_Month_Tbill  \\\n",
       "0  -0.55                        0.216              0.4              -0.12   \n",
       "1   1.06                       -0.270             -0.1               0.00   \n",
       "2   0.17                        0.108             -0.8              -0.04   \n",
       "3  -5.55                        0.001              0.8              -0.05   \n",
       "4   4.11                        0.053              0.3               0.13   \n",
       "\n",
       "   Moodys_AAA_rating   CPI  three_month_CD_rate  \\\n",
       "0       3.000000e-02  0.03                 0.02   \n",
       "1       0.000000e+00  0.04                -0.07   \n",
       "2       8.881784e-16  0.03                 0.03   \n",
       "3       1.000000e-02  0.03                -0.05   \n",
       "4       8.881784e-16 -0.16                -0.01   \n",
       "\n",
       "   Consumer_credit_Owned_and_securitized  Unemployment_rate  fitted y1  \n",
       "0                                 -0.205               -0.6   7.917657  \n",
       "1                                  0.367                0.5  -6.982639  \n",
       "2                                 -0.292               -0.3   4.286416  \n",
       "3                                  0.105                0.2  -4.802702  \n",
       "4                                 -0.079               -0.2   5.126947  "
      ]
     },
     "execution_count": 418,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df7.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 419,
   "id": "5685dd1f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept                                0.922694\n",
       "Industrial_Production_Index              0.000004\n",
       "M1_money_supply                          0.172879\n",
       "three_Month_Tbill                        0.002433\n",
       "Moodys_AAA_rating                        0.060588\n",
       "CPI                                      0.138711\n",
       "three_month_CD_rate                      0.010119\n",
       "Consumer_credit_Owned_and_securitized    0.916043\n",
       "Unemployment_rate                        0.000008\n",
       "dtype: float64"
      ]
     },
     "execution_count": 419,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model1.pvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "id": "127399e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.922693785408519,\n",
       " 3.7206362235392354e-06,\n",
       " 0.17287921602596573,\n",
       " 0.0024334618161054133,\n",
       " 0.0605875288145914,\n",
       " 0.13871050902746226,\n",
       " 0.01011861602383714,\n",
       " 0.9160433274188873,\n",
       " 7.930158033186416e-06]"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_value1 = list(model1.pvalues)\n",
    "p_value1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "id": "dfc6e4f9",
   "metadata": {},
   "outputs": [],
   "source": [
    "cols1 = df7.columns\n",
    "#redifining columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 420,
   "id": "9b685203",
   "metadata": {},
   "outputs": [],
   "source": [
    "x1 = cols1[1:]\n",
    "y1 = cols1[0:1]\n",
    "y1 = df7[y1]\n",
    "x1 = df7[x1]\n",
    "#redifining dependent and indenpendent variavbles for new data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 421,
   "id": "5a98796b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Drop the variable Consumer_credit_Owned_and_securitized\n"
     ]
    }
   ],
   "source": [
    "if max(p_value1[1:]) > 0.05:\n",
    "    max_value1 = cols1[p_value1.index(max(p_value1[1:]))]\n",
    "    print('Drop the variable ' + str(max_value1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 422,
   "id": "c3687dd9",
   "metadata": {},
   "outputs": [],
   "source": [
    "df8 = df7.drop(columns=['Consumer_credit_Owned_and_securitized','fitted y1'])\n",
    "\n",
    "model2 = ols('SandP ~ Industrial_Production_Index + M1_money_supply + three_Month_Tbill + Moodys_AAA_rating + CPI + three_month_CD_rate + Unemployment_rate',df8).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 423,
   "id": "537b8598",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SandP</th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>M1_money_supply</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>Moodys_AAA_rating</th>\n",
       "      <th>CPI</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "      <th>fitted y2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.55</td>\n",
       "      <td>0.216</td>\n",
       "      <td>0.4</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>3.000000e-02</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.02</td>\n",
       "      <td>-0.6</td>\n",
       "      <td>7.960281</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.06</td>\n",
       "      <td>-0.270</td>\n",
       "      <td>-0.1</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.04</td>\n",
       "      <td>-0.07</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-7.017797</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.17</td>\n",
       "      <td>0.108</td>\n",
       "      <td>-0.8</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>8.881784e-16</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.03</td>\n",
       "      <td>-0.3</td>\n",
       "      <td>4.311541</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-5.55</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.8</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>1.000000e-02</td>\n",
       "      <td>0.03</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>0.2</td>\n",
       "      <td>-4.813408</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.11</td>\n",
       "      <td>0.053</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.13</td>\n",
       "      <td>8.881784e-16</td>\n",
       "      <td>-0.16</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>-0.2</td>\n",
       "      <td>5.134797</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   SandP  Industrial_Production_Index  M1_money_supply  three_Month_Tbill  \\\n",
       "0  -0.55                        0.216              0.4              -0.12   \n",
       "1   1.06                       -0.270             -0.1               0.00   \n",
       "2   0.17                        0.108             -0.8              -0.04   \n",
       "3  -5.55                        0.001              0.8              -0.05   \n",
       "4   4.11                        0.053              0.3               0.13   \n",
       "\n",
       "   Moodys_AAA_rating   CPI  three_month_CD_rate  Unemployment_rate  fitted y2  \n",
       "0       3.000000e-02  0.03                 0.02               -0.6   7.960281  \n",
       "1       0.000000e+00  0.04                -0.07                0.5  -7.017797  \n",
       "2       8.881784e-16  0.03                 0.03               -0.3   4.311541  \n",
       "3       1.000000e-02  0.03                -0.05                0.2  -4.813408  \n",
       "4       8.881784e-16 -0.16                -0.01               -0.2   5.134797  "
      ]
     },
     "execution_count": 423,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "forecasted_y2 = model2.fittedvalues\n",
    "df8.loc[:,'fitted y2'] = forecasted_y2\n",
    "df8.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 424,
   "id": "73fd7a5d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept                      0.922965\n",
       "Industrial_Production_Index    0.000004\n",
       "M1_money_supply                0.168770\n",
       "three_Month_Tbill              0.002387\n",
       "Moodys_AAA_rating              0.060709\n",
       "CPI                            0.131214\n",
       "three_month_CD_rate            0.009907\n",
       "Unemployment_rate              0.000006\n",
       "dtype: float64"
      ]
     },
     "execution_count": 424,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model2.pvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 425,
   "id": "fb781598",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Drop the variable M1_money_supply\n"
     ]
    }
   ],
   "source": [
    "p_value2 = list(model2.pvalues)\n",
    "cols2 = df8.columns\n",
    "\n",
    "x2 = cols2[1:]\n",
    "y2 = cols2[0:1]\n",
    "y2 = df8[y2]\n",
    "x2 = df8[x2]\n",
    "\n",
    "if max(p_value2[1:]) > 0.05:\n",
    "    max_value2 = cols2[p_value2.index(max(p_value2[1:]))]\n",
    "    print('Drop the variable ' + str(max_value2))\n",
    "else:\n",
    "    print('No variable to be dropped')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "id": "34f74f37",
   "metadata": {},
   "outputs": [],
   "source": [
    "df9 = df8.drop(columns=['M1_money_supply','fitted y2'])\n",
    "\n",
    "model3 = ols('SandP ~ Industrial_Production_Index + three_Month_Tbill + Moodys_AAA_rating + CPI + three_month_CD_rate + Unemployment_rate',df9).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 426,
   "id": "72cf7365",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SandP</th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>Moodys_AAA_rating</th>\n",
       "      <th>CPI</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "      <th>fitted y3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.55</td>\n",
       "      <td>0.216</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>3.000000e-02</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.02</td>\n",
       "      <td>-0.6</td>\n",
       "      <td>6.052422</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.06</td>\n",
       "      <td>-0.270</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.04</td>\n",
       "      <td>-0.07</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-5.310740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.17</td>\n",
       "      <td>0.108</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>8.881784e-16</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.03</td>\n",
       "      <td>-0.3</td>\n",
       "      <td>3.396579</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-5.55</td>\n",
       "      <td>0.001</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>1.000000e-02</td>\n",
       "      <td>0.03</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>0.2</td>\n",
       "      <td>-4.078397</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.11</td>\n",
       "      <td>0.053</td>\n",
       "      <td>0.13</td>\n",
       "      <td>8.881784e-16</td>\n",
       "      <td>-0.16</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>-0.2</td>\n",
       "      <td>4.385856</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   SandP  Industrial_Production_Index  three_Month_Tbill  Moodys_AAA_rating  \\\n",
       "0  -0.55                        0.216              -0.12       3.000000e-02   \n",
       "1   1.06                       -0.270               0.00       0.000000e+00   \n",
       "2   0.17                        0.108              -0.04       8.881784e-16   \n",
       "3  -5.55                        0.001              -0.05       1.000000e-02   \n",
       "4   4.11                        0.053               0.13       8.881784e-16   \n",
       "\n",
       "    CPI  three_month_CD_rate  Unemployment_rate  fitted y3  \n",
       "0  0.03                 0.02               -0.6   6.052422  \n",
       "1  0.04                -0.07                0.5  -5.310740  \n",
       "2  0.03                 0.03               -0.3   3.396579  \n",
       "3  0.03                -0.05                0.2  -4.078397  \n",
       "4 -0.16                -0.01               -0.2   4.385856  "
      ]
     },
     "execution_count": 426,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "forecasted_y3 = model3.fittedvalues\n",
    "df9.loc[:,'fitted y3'] = forecasted_y3\n",
    "df9.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 427,
   "id": "1e134ecf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept                      0.947401\n",
       "Industrial_Production_Index    0.000004\n",
       "three_Month_Tbill              0.002853\n",
       "Moodys_AAA_rating              0.052940\n",
       "CPI                            0.099122\n",
       "three_month_CD_rate            0.013106\n",
       "Unemployment_rate              0.000009\n",
       "dtype: float64"
      ]
     },
     "execution_count": 427,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model3.pvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 428,
   "id": "4a64a56a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Drop the variable CPI\n"
     ]
    }
   ],
   "source": [
    "p_value3 = list(model3.pvalues)\n",
    "cols3 = df9.columns\n",
    "\n",
    "x3 = cols3[1:]\n",
    "y3 = cols3[0:1]\n",
    "y3 = df9[y3]\n",
    "x3 = df9[x3]\n",
    "\n",
    "if max(p_value3[1:]) > 0.05:\n",
    "    max_value3 = cols3[p_value3.index(max(p_value3[1:]))]\n",
    "    print('Drop the variable ' + str(max_value3))\n",
    "else:\n",
    "    print('No variable to be dropped')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 429,
   "id": "04938ee9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'CPI'"
      ]
     },
     "execution_count": 429,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max_value3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 430,
   "id": "02f6fa1c",
   "metadata": {},
   "outputs": [],
   "source": [
    "df9_1 = df9.drop(columns=['CPI','fitted y3'])\n",
    "\n",
    "model3_1 = ols('SandP ~ Industrial_Production_Index + three_Month_Tbill + Moodys_AAA_rating + three_month_CD_rate + Unemployment_rate',df9_1).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 431,
   "id": "0aa89881",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept                      0.954101\n",
       "Industrial_Production_Index    0.000004\n",
       "three_Month_Tbill              0.004206\n",
       "Moodys_AAA_rating              0.062772\n",
       "three_month_CD_rate            0.017664\n",
       "Unemployment_rate              0.000004\n",
       "dtype: float64"
      ]
     },
     "execution_count": 431,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model3_1.pvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 432,
   "id": "484b8918",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Drop the variable Moodys_AAA_rating\n"
     ]
    }
   ],
   "source": [
    "p_value_31 = list(model3_1.pvalues)\n",
    "cols3_1 = df9_1.columns\n",
    "\n",
    "x3_1 = cols3_1[1:]\n",
    "y3_1 = cols3_1[0:1]\n",
    "y3_1 = df9_1[y3_1]\n",
    "x3_1 = df9_1[x3_1]\n",
    "\n",
    "if max(p_value_31[1:]) > 0.05:\n",
    "    max_value3_1 = cols3_1[p_value_31.index(max(p_value_31[1:]))]\n",
    "    print('Drop the variable ' + str(max_value3_1))\n",
    "else:\n",
    "    print('No variable to be dropped')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 433,
   "id": "c50477c1",
   "metadata": {},
   "outputs": [],
   "source": [
    "df9_2 = df9_1.drop(columns=['Moodys_AAA_rating'])\n",
    "\n",
    "model3_2 = ols('SandP ~ Industrial_Production_Index + three_Month_Tbill + three_month_CD_rate + Unemployment_rate',df9_2).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 434,
   "id": "44f0e8e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept                      0.956373\n",
       "Industrial_Production_Index    0.000003\n",
       "three_Month_Tbill              0.009726\n",
       "three_month_CD_rate            0.005888\n",
       "Unemployment_rate              0.000007\n",
       "dtype: float64"
      ]
     },
     "execution_count": 434,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model3_2.pvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 435,
   "id": "ebefc163",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>SandP</td>      <th>  R-squared:         </th> <td>   0.053</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.047</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   9.399</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sun, 31 Oct 2021</td> <th>  Prob (F-statistic):</th> <td>2.14e-07</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>18:46:21</td>     <th>  Log-Likelihood:    </th> <td> -3514.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   676</td>      <th>  AIC:               </th> <td>   7040.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   671</td>      <th>  BIC:               </th> <td>   7062.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     4</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "               <td></td>                  <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>                   <td>   -0.0927</td> <td>    1.693</td> <td>   -0.055</td> <td> 0.956</td> <td>   -3.417</td> <td>    3.232</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Industrial_Production_Index</th> <td>  -11.3407</td> <td>    2.414</td> <td>   -4.697</td> <td> 0.000</td> <td>  -16.081</td> <td>   -6.600</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>three_Month_Tbill</th>           <td>   14.9487</td> <td>    5.765</td> <td>    2.593</td> <td> 0.010</td> <td>    3.628</td> <td>   26.269</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>three_month_CD_rate</th>         <td>  -12.8573</td> <td>    4.654</td> <td>   -2.763</td> <td> 0.006</td> <td>  -21.995</td> <td>   -3.720</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Unemployment_rate</th>           <td>  -18.6979</td> <td>    4.135</td> <td>   -4.522</td> <td> 0.000</td> <td>  -26.816</td> <td>  -10.580</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>87.634</td> <th>  Durbin-Watson:     </th> <td>   2.813</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td> 836.177</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.034</td> <th>  Prob(JB):          </th> <td>2.67e-182</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 8.448</td> <th>  Cond. No.          </th> <td>    4.20</td> \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                  SandP   R-squared:                       0.053\n",
       "Model:                            OLS   Adj. R-squared:                  0.047\n",
       "Method:                 Least Squares   F-statistic:                     9.399\n",
       "Date:                Sun, 31 Oct 2021   Prob (F-statistic):           2.14e-07\n",
       "Time:                        18:46:21   Log-Likelihood:                -3514.8\n",
       "No. Observations:                 676   AIC:                             7040.\n",
       "Df Residuals:                     671   BIC:                             7062.\n",
       "Df Model:                           4                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "===============================================================================================\n",
       "                                  coef    std err          t      P>|t|      [0.025      0.975]\n",
       "-----------------------------------------------------------------------------------------------\n",
       "Intercept                      -0.0927      1.693     -0.055      0.956      -3.417       3.232\n",
       "Industrial_Production_Index   -11.3407      2.414     -4.697      0.000     -16.081      -6.600\n",
       "three_Month_Tbill              14.9487      5.765      2.593      0.010       3.628      26.269\n",
       "three_month_CD_rate           -12.8573      4.654     -2.763      0.006     -21.995      -3.720\n",
       "Unemployment_rate             -18.6979      4.135     -4.522      0.000     -26.816     -10.580\n",
       "==============================================================================\n",
       "Omnibus:                       87.634   Durbin-Watson:                   2.813\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              836.177\n",
       "Skew:                          -0.034   Prob(JB):                    2.67e-182\n",
       "Kurtosis:                       8.448   Cond. No.                         4.20\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 435,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model3_2.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 436,
   "id": "31411fde",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SandP</th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.55</td>\n",
       "      <td>0.216</td>\n",
       "      <td>-1.200000e-01</td>\n",
       "      <td>2.000000e-02</td>\n",
       "      <td>-0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.06</td>\n",
       "      <td>-0.270</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>-7.000000e-02</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.17</td>\n",
       "      <td>0.108</td>\n",
       "      <td>-4.000000e-02</td>\n",
       "      <td>3.000000e-02</td>\n",
       "      <td>-0.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-5.55</td>\n",
       "      <td>0.001</td>\n",
       "      <td>-5.000000e-02</td>\n",
       "      <td>-5.000000e-02</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.11</td>\n",
       "      <td>0.053</td>\n",
       "      <td>1.300000e-01</td>\n",
       "      <td>-1.000000e-02</td>\n",
       "      <td>-0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>673</th>\n",
       "      <td>203.59</td>\n",
       "      <td>-2.697</td>\n",
       "      <td>3.469447e-18</td>\n",
       "      <td>2.000000e-02</td>\n",
       "      <td>0.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>674</th>\n",
       "      <td>-204.00</td>\n",
       "      <td>0.552</td>\n",
       "      <td>1.000000e-02</td>\n",
       "      <td>-2.000000e-02</td>\n",
       "      <td>-0.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>675</th>\n",
       "      <td>43.97</td>\n",
       "      <td>-0.130</td>\n",
       "      <td>2.000000e-02</td>\n",
       "      <td>-1.387779e-17</td>\n",
       "      <td>0.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>676</th>\n",
       "      <td>54.58</td>\n",
       "      <td>0.357</td>\n",
       "      <td>-1.000000e-02</td>\n",
       "      <td>2.000000e-02</td>\n",
       "      <td>-0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>677</th>\n",
       "      <td>-34.72</td>\n",
       "      <td>-0.439</td>\n",
       "      <td>-1.000000e-02</td>\n",
       "      <td>-1.000000e-02</td>\n",
       "      <td>0.3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>676 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      SandP  Industrial_Production_Index  three_Month_Tbill  \\\n",
       "0     -0.55                        0.216      -1.200000e-01   \n",
       "1      1.06                       -0.270       0.000000e+00   \n",
       "2      0.17                        0.108      -4.000000e-02   \n",
       "3     -5.55                        0.001      -5.000000e-02   \n",
       "4      4.11                        0.053       1.300000e-01   \n",
       "..      ...                          ...                ...   \n",
       "673  203.59                       -2.697       3.469447e-18   \n",
       "674 -204.00                        0.552       1.000000e-02   \n",
       "675   43.97                       -0.130       2.000000e-02   \n",
       "676   54.58                        0.357      -1.000000e-02   \n",
       "677  -34.72                       -0.439      -1.000000e-02   \n",
       "\n",
       "     three_month_CD_rate  Unemployment_rate  \n",
       "0           2.000000e-02               -0.6  \n",
       "1          -7.000000e-02                0.5  \n",
       "2           3.000000e-02               -0.3  \n",
       "3          -5.000000e-02                0.2  \n",
       "4          -1.000000e-02               -0.2  \n",
       "..                   ...                ...  \n",
       "673         2.000000e-02                0.3  \n",
       "674        -2.000000e-02               -0.4  \n",
       "675        -1.387779e-17                0.4  \n",
       "676         2.000000e-02               -0.6  \n",
       "677        -1.000000e-02                0.3  \n",
       "\n",
       "[676 rows x 5 columns]"
      ]
     },
     "execution_count": 436,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df9_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 437,
   "id": "e0933819",
   "metadata": {},
   "outputs": [],
   "source": [
    "cols3_2 = df9_2.columns\n",
    "\n",
    "x3_2 = cols3_2[1:]\n",
    "y3_2 = cols3_2[0:1]\n",
    "y3_2 = df9_2[y3_2]\n",
    "x3_2 = df9_2[x3_2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "42d1b0f0",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "c5a80b0d",
   "metadata": {},
   "source": [
    "### Multicollinearity Check"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "75efe18a",
   "metadata": {},
   "outputs": [],
   "source": [
    "#now for calculating VIF, we'll add a constant to our independent variables data, i.e. an intercept"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 438,
   "id": "4c082ec3",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_m = add_constant(x3_2)\n",
    "cols_m = x_m.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 439,
   "id": "2c8a6704",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.0009830073613823,\n",
       " 1.6038546778075322,\n",
       " 2.889548707788511,\n",
       " 2.901249810736872,\n",
       " 1.595488052863333]"
      ]
     },
     "execution_count": 439,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vif_1 = [variance_inflation_factor(x_m.values,j) for j in range(x_m.shape[1])]\n",
    "\n",
    "#storing in a variable - VIF\n",
    "#https://stackoverflow.com/questions/42658379/variance-inflation-factor-in-python\n",
    "vif_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 440,
   "id": "f32d004a",
   "metadata": {},
   "outputs": [],
   "source": [
    "vif_12 = vif_1[1:]\n",
    "#the first VIF belongs to the constant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 441,
   "id": "7e06e802",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.901249810736872"
      ]
     },
     "execution_count": 441,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(vif_12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "314c3207",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Since maximum vif is less than 5 percent, it means that there is no variable with vif greater than 5 percent\n",
    "#it means that there is no problem of multicollinearity in our data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c471b85",
   "metadata": {},
   "source": [
    "### Autocorrelation check (Durbin Watson test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "187f92ab",
   "metadata": {},
   "outputs": [],
   "source": [
    "#we will store the error terms in a variable - say 'error'\n",
    "#store the lag1 term of the error - error_lag1, \n",
    "#the error term 'error' becomes the DEPENDENT variable, error lag 1 becomes independent variable and remaining independent variables are independent only\n",
    "#then find p value\n",
    "#if p value of error lag 1 is less than 5 percent, we reject the null and say that problem of autocorrelation exist \n",
    "#this is called the breusch godfrey test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 442,
   "id": "444fb22d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.812859807281086"
      ]
     },
     "execution_count": 442,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "durbin_watson(model3_2.resid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "e56cc4d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Since the DB watson test statistic is more than 2, it indicates negative autocorrelation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 443,
   "id": "880c00a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0       -7.175521\n",
       "1        6.539626\n",
       "2       -3.138259\n",
       "3       -1.601849\n",
       "4       -1.007771\n",
       "          ...    \n",
       "673    178.963401\n",
       "674   -205.533093\n",
       "675     49.768565\n",
       "676     47.909159\n",
       "677    -33.975605\n",
       "Length: 676, dtype: float64"
      ]
     },
     "execution_count": 443,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "error = model3_2.resid\n",
    "error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 444,
   "id": "79d871e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0             NaN\n",
       "1       -7.175521\n",
       "2        6.539626\n",
       "3       -3.138259\n",
       "4       -1.601849\n",
       "          ...    \n",
       "673      0.935246\n",
       "674    178.963401\n",
       "675   -205.533093\n",
       "676     49.768565\n",
       "677     47.909159\n",
       "Length: 676, dtype: float64"
      ]
     },
     "execution_count": 444,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "errorlag1 = error.shift(1)\n",
    "errorlag1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 445,
   "id": "d950d670",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0        0.000000\n",
       "1       -7.175521\n",
       "2        6.539626\n",
       "3       -3.138259\n",
       "4       -1.601849\n",
       "          ...    \n",
       "673      0.935246\n",
       "674    178.963401\n",
       "675   -205.533093\n",
       "676     49.768565\n",
       "677     47.909159\n",
       "Length: 676, dtype: float64"
      ]
     },
     "execution_count": 445,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "errorlag1[0] = 0\n",
    "errorlag1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "id": "86ba5468",
   "metadata": {},
   "outputs": [],
   "source": [
    "#x3_2.loc[:,'error'] = error\n",
    "#x3_2.loc[:,'errorlag1'] = errorlag1\n",
    "#loc function slices the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 446,
   "id": "8ad2cbe2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.216</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>0.02</td>\n",
       "      <td>-0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.270</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-0.07</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.108</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>0.03</td>\n",
       "      <td>-0.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.001</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.053</td>\n",
       "      <td>0.13</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>-0.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Industrial_Production_Index  three_Month_Tbill  three_month_CD_rate  \\\n",
       "0                        0.216              -0.12                 0.02   \n",
       "1                       -0.270               0.00                -0.07   \n",
       "2                        0.108              -0.04                 0.03   \n",
       "3                        0.001              -0.05                -0.05   \n",
       "4                        0.053               0.13                -0.01   \n",
       "\n",
       "   Unemployment_rate  \n",
       "0               -0.6  \n",
       "1                0.5  \n",
       "2               -0.3  \n",
       "3                0.2  \n",
       "4               -0.2  "
      ]
     },
     "execution_count": 446,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x3_2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 447,
   "id": "a6df3c3b",
   "metadata": {},
   "outputs": [],
   "source": [
    "df9_3 = pd.concat([y3_2,x3_2],axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 448,
   "id": "01b27ced",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SandP</th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.55</td>\n",
       "      <td>0.216</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>0.02</td>\n",
       "      <td>-0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.06</td>\n",
       "      <td>-0.270</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-0.07</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.17</td>\n",
       "      <td>0.108</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>0.03</td>\n",
       "      <td>-0.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-5.55</td>\n",
       "      <td>0.001</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.11</td>\n",
       "      <td>0.053</td>\n",
       "      <td>0.13</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>-0.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   SandP  Industrial_Production_Index  three_Month_Tbill  three_month_CD_rate  \\\n",
       "0  -0.55                        0.216              -0.12                 0.02   \n",
       "1   1.06                       -0.270               0.00                -0.07   \n",
       "2   0.17                        0.108              -0.04                 0.03   \n",
       "3  -5.55                        0.001              -0.05                -0.05   \n",
       "4   4.11                        0.053               0.13                -0.01   \n",
       "\n",
       "   Unemployment_rate  \n",
       "0               -0.6  \n",
       "1                0.5  \n",
       "2               -0.3  \n",
       "3                0.2  \n",
       "4               -0.2  "
      ]
     },
     "execution_count": 448,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df9_3.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c4bab5e",
   "metadata": {},
   "source": [
    "### Cochrane-Orcutt Procedure for treating Autocorrelation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 449,
   "id": "a5dcc1a6",
   "metadata": {},
   "outputs": [],
   "source": [
    "model5 = ols('error ~ errorlag1',df9_3).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 450,
   "id": "5909d0d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>error</td>      <th>  R-squared:         </th> <td>   0.166</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.164</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   133.9</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sun, 31 Oct 2021</td> <th>  Prob (F-statistic):</th> <td>2.28e-28</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>18:48:37</td>     <th>  Log-Likelihood:    </th> <td> -3453.6</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   676</td>      <th>  AIC:               </th> <td>   6911.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   674</td>      <th>  BIC:               </th> <td>   6920.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>    0.0205</td> <td>    1.542</td> <td>    0.013</td> <td> 0.989</td> <td>   -3.008</td> <td>    3.049</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>errorlag1</th> <td>   -0.4073</td> <td>    0.035</td> <td>  -11.570</td> <td> 0.000</td> <td>   -0.476</td> <td>   -0.338</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>90.715</td> <th>  Durbin-Watson:     </th> <td>   2.243</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td> 902.812</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.079</td> <th>  Prob(JB):          </th> <td>9.06e-197</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 8.659</td> <th>  Cond. No.          </th> <td>    43.8</td> \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                  error   R-squared:                       0.166\n",
       "Model:                            OLS   Adj. R-squared:                  0.164\n",
       "Method:                 Least Squares   F-statistic:                     133.9\n",
       "Date:                Sun, 31 Oct 2021   Prob (F-statistic):           2.28e-28\n",
       "Time:                        18:48:37   Log-Likelihood:                -3453.6\n",
       "No. Observations:                 676   AIC:                             6911.\n",
       "Df Residuals:                     674   BIC:                             6920.\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      0.0205      1.542      0.013      0.989      -3.008       3.049\n",
       "errorlag1     -0.4073      0.035    -11.570      0.000      -0.476      -0.338\n",
       "==============================================================================\n",
       "Omnibus:                       90.715   Durbin-Watson:                   2.243\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              902.812\n",
       "Skew:                           0.079   Prob(JB):                    9.06e-197\n",
       "Kurtosis:                       8.659   Cond. No.                         43.8\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 450,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model5.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "65ed7629",
   "metadata": {},
   "outputs": [],
   "source": [
    "# we get r = -0.4073"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 451,
   "id": "b3fbec4e",
   "metadata": {},
   "outputs": [],
   "source": [
    "ytminus = y3_2.shift(1)\n",
    "ytminus1 = ytminus.bfill()\n",
    "\n",
    "xtminus = x3_2.shift(1)\n",
    "xtminus1 = xtminus.bfill()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 452,
   "id": "2ae4dbbc",
   "metadata": {},
   "outputs": [],
   "source": [
    "df10_1 = df9_3.drop(columns=['SandP','Industrial_Production_Index','three_Month_Tbill','three_month_CD_rate','Unemployment_rate'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 453,
   "id": "20f397f5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SandP</th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.55</td>\n",
       "      <td>0.216</td>\n",
       "      <td>-1.200000e-01</td>\n",
       "      <td>2.000000e-02</td>\n",
       "      <td>-0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.55</td>\n",
       "      <td>0.216</td>\n",
       "      <td>-1.200000e-01</td>\n",
       "      <td>2.000000e-02</td>\n",
       "      <td>-0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.06</td>\n",
       "      <td>-0.270</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>-7.000000e-02</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.17</td>\n",
       "      <td>0.108</td>\n",
       "      <td>-4.000000e-02</td>\n",
       "      <td>3.000000e-02</td>\n",
       "      <td>-0.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-5.55</td>\n",
       "      <td>0.001</td>\n",
       "      <td>-5.000000e-02</td>\n",
       "      <td>-5.000000e-02</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>673</th>\n",
       "      <td>-62.60</td>\n",
       "      <td>5.776</td>\n",
       "      <td>3.000000e-02</td>\n",
       "      <td>2.000000e-02</td>\n",
       "      <td>-0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>674</th>\n",
       "      <td>203.59</td>\n",
       "      <td>-2.697</td>\n",
       "      <td>3.469447e-18</td>\n",
       "      <td>2.000000e-02</td>\n",
       "      <td>0.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>675</th>\n",
       "      <td>-204.00</td>\n",
       "      <td>0.552</td>\n",
       "      <td>1.000000e-02</td>\n",
       "      <td>-2.000000e-02</td>\n",
       "      <td>-0.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>676</th>\n",
       "      <td>43.97</td>\n",
       "      <td>-0.130</td>\n",
       "      <td>2.000000e-02</td>\n",
       "      <td>-1.387779e-17</td>\n",
       "      <td>0.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>677</th>\n",
       "      <td>54.58</td>\n",
       "      <td>0.357</td>\n",
       "      <td>-1.000000e-02</td>\n",
       "      <td>2.000000e-02</td>\n",
       "      <td>-0.6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>676 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      SandP  Industrial_Production_Index  three_Month_Tbill  \\\n",
       "0     -0.55                        0.216      -1.200000e-01   \n",
       "1     -0.55                        0.216      -1.200000e-01   \n",
       "2      1.06                       -0.270       0.000000e+00   \n",
       "3      0.17                        0.108      -4.000000e-02   \n",
       "4     -5.55                        0.001      -5.000000e-02   \n",
       "..      ...                          ...                ...   \n",
       "673  -62.60                        5.776       3.000000e-02   \n",
       "674  203.59                       -2.697       3.469447e-18   \n",
       "675 -204.00                        0.552       1.000000e-02   \n",
       "676   43.97                       -0.130       2.000000e-02   \n",
       "677   54.58                        0.357      -1.000000e-02   \n",
       "\n",
       "     three_month_CD_rate  Unemployment_rate  \n",
       "0           2.000000e-02               -0.6  \n",
       "1           2.000000e-02               -0.6  \n",
       "2          -7.000000e-02                0.5  \n",
       "3           3.000000e-02               -0.3  \n",
       "4          -5.000000e-02                0.2  \n",
       "..                   ...                ...  \n",
       "673         2.000000e-02               -0.1  \n",
       "674         2.000000e-02                0.3  \n",
       "675        -2.000000e-02               -0.4  \n",
       "676        -1.387779e-17                0.4  \n",
       "677         2.000000e-02               -0.6  \n",
       "\n",
       "[676 rows x 5 columns]"
      ]
     },
     "execution_count": 453,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df10_1 = pd.concat([ytminus1,xtminus1],axis = 1)\n",
    "df10_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "id": "a7077bb2",
   "metadata": {},
   "outputs": [],
   "source": [
    "#cols5 = df10.columns\n",
    "\n",
    "#x5 = cols5[1:5]\n",
    "#y5 = cols5[0:1]\n",
    "#y5 = df10[y5]\n",
    "#x5 = df10[x5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 260,
   "id": "54626507",
   "metadata": {},
   "outputs": [],
   "source": [
    "#x5.loc[:,'ytminus1'] = ytminus1\n",
    "#df10 = pd.concat([y5,x5],axis = 1)\n",
    "#ytminus1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 454,
   "id": "1de80800",
   "metadata": {},
   "outputs": [],
   "source": [
    "r_ytminus1 = (-0.4073)*df10_1['SandP']\n",
    "r_IPI = (-0.4073)*df10_1['Industrial_Production_Index']\n",
    "r_tbill = (-0.4073)*df10_1['three_Month_Tbill']\n",
    "r_cd = (-0.4073)*df10_1['three_month_CD_rate']\n",
    "r_unemp = (-0.4073)*df10_1['Unemployment_rate']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 455,
   "id": "574d2c52",
   "metadata": {},
   "outputs": [],
   "source": [
    "transformed_y3_2 = df9_3['SandP'] - r_ytminus1\n",
    "transformed_IPI = df9_3['Industrial_Production_Index'] - r_IPI\n",
    "transformed_tbill = df9_3['three_Month_Tbill'] - r_tbill\n",
    "transformed_cd = df9_3['three_month_CD_rate'] - r_cd\n",
    "transformed_un = df9_3['Unemployment_rate'] - r_unemp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 456,
   "id": "1cea3ab9",
   "metadata": {},
   "outputs": [],
   "source": [
    "df10_2 = pd.concat([transformed_y3_2,transformed_IPI, transformed_tbill, transformed_cd,transformed_un],axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 457,
   "id": "f2659557",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SandP</th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.774015</td>\n",
       "      <td>0.303977</td>\n",
       "      <td>-0.168876</td>\n",
       "      <td>0.028146</td>\n",
       "      <td>-0.84438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.835985</td>\n",
       "      <td>-0.182023</td>\n",
       "      <td>-0.048876</td>\n",
       "      <td>-0.061854</td>\n",
       "      <td>0.25562</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.601738</td>\n",
       "      <td>-0.001971</td>\n",
       "      <td>-0.040000</td>\n",
       "      <td>0.001489</td>\n",
       "      <td>-0.09635</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-5.480759</td>\n",
       "      <td>0.044988</td>\n",
       "      <td>-0.066292</td>\n",
       "      <td>-0.037781</td>\n",
       "      <td>0.07781</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.849485</td>\n",
       "      <td>0.053407</td>\n",
       "      <td>0.109635</td>\n",
       "      <td>-0.030365</td>\n",
       "      <td>-0.11854</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      SandP  Industrial_Production_Index  three_Month_Tbill  \\\n",
       "0 -0.774015                     0.303977          -0.168876   \n",
       "1  0.835985                    -0.182023          -0.048876   \n",
       "2  0.601738                    -0.001971          -0.040000   \n",
       "3 -5.480759                     0.044988          -0.066292   \n",
       "4  1.849485                     0.053407           0.109635   \n",
       "\n",
       "   three_month_CD_rate  Unemployment_rate  \n",
       "0             0.028146           -0.84438  \n",
       "1            -0.061854            0.25562  \n",
       "2             0.001489           -0.09635  \n",
       "3            -0.037781            0.07781  \n",
       "4            -0.030365           -0.11854  "
      ]
     },
     "execution_count": 457,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df10_2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 458,
   "id": "aac711c3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>    <td>transformed_y3_2</td> <th>  R-squared:         </th> <td>   0.041</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.036</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   7.262</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sun, 31 Oct 2021</td> <th>  Prob (F-statistic):</th> <td>9.97e-06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>18:54:21</td>     <th>  Log-Likelihood:    </th> <td> -3453.0</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   676</td>      <th>  AIC:               </th> <td>   6916.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   671</td>      <th>  BIC:               </th> <td>   6939.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     4</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "          <td></td>             <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>         <td>   -0.0676</td> <td>    1.546</td> <td>   -0.044</td> <td> 0.965</td> <td>   -3.103</td> <td>    2.968</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>transformed_IPI</th>   <td>   -9.6982</td> <td>    2.536</td> <td>   -3.824</td> <td> 0.000</td> <td>  -14.678</td> <td>   -4.718</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>transformed_tbill</th> <td>   17.7724</td> <td>    5.845</td> <td>    3.041</td> <td> 0.002</td> <td>    6.296</td> <td>   29.249</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>transformed_cd</th>    <td>  -15.6956</td> <td>    4.738</td> <td>   -3.313</td> <td> 0.001</td> <td>  -24.999</td> <td>   -6.393</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>transformed_un</th>    <td>  -14.7124</td> <td>    4.217</td> <td>   -3.489</td> <td> 0.001</td> <td>  -22.992</td> <td>   -6.433</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>91.732</td> <th>  Durbin-Watson:     </th> <td>   2.251</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td> 939.206</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.060</td> <th>  Prob(JB):          </th> <td>1.13e-204</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 8.773</td> <th>  Cond. No.          </th> <td>    4.79</td> \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:       transformed_y3_2   R-squared:                       0.041\n",
       "Model:                            OLS   Adj. R-squared:                  0.036\n",
       "Method:                 Least Squares   F-statistic:                     7.262\n",
       "Date:                Sun, 31 Oct 2021   Prob (F-statistic):           9.97e-06\n",
       "Time:                        18:54:21   Log-Likelihood:                -3453.0\n",
       "No. Observations:                 676   AIC:                             6916.\n",
       "Df Residuals:                     671   BIC:                             6939.\n",
       "Df Model:                           4                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "=====================================================================================\n",
       "                        coef    std err          t      P>|t|      [0.025      0.975]\n",
       "-------------------------------------------------------------------------------------\n",
       "Intercept            -0.0676      1.546     -0.044      0.965      -3.103       2.968\n",
       "transformed_IPI      -9.6982      2.536     -3.824      0.000     -14.678      -4.718\n",
       "transformed_tbill    17.7724      5.845      3.041      0.002       6.296      29.249\n",
       "transformed_cd      -15.6956      4.738     -3.313      0.001     -24.999      -6.393\n",
       "transformed_un      -14.7124      4.217     -3.489      0.001     -22.992      -6.433\n",
       "==============================================================================\n",
       "Omnibus:                       91.732   Durbin-Watson:                   2.251\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              939.206\n",
       "Skew:                           0.060   Prob(JB):                    1.13e-204\n",
       "Kurtosis:                       8.773   Cond. No.                         4.79\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 458,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model5_1 = ols('transformed_y3_2 ~ transformed_IPI + transformed_tbill + transformed_cd + transformed_un',df10_2).fit()\n",
    "model5_1.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "id": "08fcf8d8",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Since Durbin watson statistic is now close to 2, we can say that autocorrelation problem has been removed by some extent"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c17fccf",
   "metadata": {},
   "source": [
    "### Autoregressive model for correcting autocorrelation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "id": "5df46b4d",
   "metadata": {},
   "outputs": [],
   "source": [
    "#model6 = ols('SandP ~ Industrial_Production_Index + three_Month_Tbill + three_month_CD_rate + Unemployment_rate + ytminus1',df10).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9ccb8029",
   "metadata": {},
   "outputs": [],
   "source": [
    "#model6.pvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 278,
   "id": "b15c4fbc",
   "metadata": {},
   "outputs": [],
   "source": [
    "#durbin_watson(model6.resid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "id": "badad627",
   "metadata": {},
   "outputs": [],
   "source": [
    "#since p value of ytminus1 is less than 5 percent, it means that is a significant indpendent variable"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c654760d",
   "metadata": {},
   "source": [
    "### Linearity Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "60c67c57",
   "metadata": {},
   "outputs": [],
   "source": [
    "#error1 = model6.resid\n",
    "#error1lag1 = error1.shift(1)\n",
    "#error1lag1[0] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c9b26453",
   "metadata": {},
   "outputs": [],
   "source": [
    "#introduce x6 and y6 and then add error variables in it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 514,
   "id": "bcddae61",
   "metadata": {},
   "outputs": [],
   "source": [
    "df12 = df10_2 + 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 515,
   "id": "6ed62966",
   "metadata": {},
   "outputs": [],
   "source": [
    "cols6 = df12.columns\n",
    "\n",
    "x6 = cols6[1:]\n",
    "y6 = cols6[0:1]\n",
    "y6 = df12[y6]\n",
    "x6 = df12[x6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 510,
   "id": "1aca01a4",
   "metadata": {},
   "outputs": [],
   "source": [
    "#ytminus_y6 = y6.shift(1)\n",
    "#ytminus1_y6 = ytminus_y6.bfill()\n",
    "#ytminus1_y6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 516,
   "id": "2f7536c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "df12 = pd.concat([y6,x6],axis = 1)\n",
    "#add ytminus1 column also to df12\n",
    "#df12.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 283,
   "id": "f2e5a47c",
   "metadata": {},
   "outputs": [],
   "source": [
    "#model7 = ols('error1 ~ Industrial_Production_Index + three_Month_Tbill + three_month_CD_rate + Unemployment_rate + ytminus1_y6 + error1lag1',df12).fit()\n",
    "#model7.pvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 324,
   "id": "62b9add7",
   "metadata": {},
   "outputs": [],
   "source": [
    "#the p value of error1lag1 is less than 5 percent, it means the problem of autocorrelation is still there. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 517,
   "id": "01280bbc",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SandP</th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.774015</td>\n",
       "      <td>0.303977</td>\n",
       "      <td>-0.168876</td>\n",
       "      <td>0.028146</td>\n",
       "      <td>-0.84438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.835985</td>\n",
       "      <td>-0.182023</td>\n",
       "      <td>-0.048876</td>\n",
       "      <td>-0.061854</td>\n",
       "      <td>0.25562</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.601738</td>\n",
       "      <td>-0.001971</td>\n",
       "      <td>-0.040000</td>\n",
       "      <td>0.001489</td>\n",
       "      <td>-0.09635</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-5.480759</td>\n",
       "      <td>0.044988</td>\n",
       "      <td>-0.066292</td>\n",
       "      <td>-0.037781</td>\n",
       "      <td>0.07781</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.849485</td>\n",
       "      <td>0.053407</td>\n",
       "      <td>0.109635</td>\n",
       "      <td>-0.030365</td>\n",
       "      <td>-0.11854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>673</th>\n",
       "      <td>178.093020</td>\n",
       "      <td>-0.344435</td>\n",
       "      <td>0.012219</td>\n",
       "      <td>0.028146</td>\n",
       "      <td>0.25927</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>674</th>\n",
       "      <td>-121.077793</td>\n",
       "      <td>-0.546488</td>\n",
       "      <td>0.010000</td>\n",
       "      <td>-0.011854</td>\n",
       "      <td>-0.27781</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>675</th>\n",
       "      <td>-39.119200</td>\n",
       "      <td>0.094830</td>\n",
       "      <td>0.024073</td>\n",
       "      <td>-0.008146</td>\n",
       "      <td>0.23708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>676</th>\n",
       "      <td>72.488981</td>\n",
       "      <td>0.304051</td>\n",
       "      <td>-0.001854</td>\n",
       "      <td>0.020000</td>\n",
       "      <td>-0.43708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>677</th>\n",
       "      <td>-12.489566</td>\n",
       "      <td>-0.293594</td>\n",
       "      <td>-0.014073</td>\n",
       "      <td>-0.001854</td>\n",
       "      <td>0.05562</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>676 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          SandP  Industrial_Production_Index  three_Month_Tbill  \\\n",
       "0     -0.774015                     0.303977          -0.168876   \n",
       "1      0.835985                    -0.182023          -0.048876   \n",
       "2      0.601738                    -0.001971          -0.040000   \n",
       "3     -5.480759                     0.044988          -0.066292   \n",
       "4      1.849485                     0.053407           0.109635   \n",
       "..          ...                          ...                ...   \n",
       "673  178.093020                    -0.344435           0.012219   \n",
       "674 -121.077793                    -0.546488           0.010000   \n",
       "675  -39.119200                     0.094830           0.024073   \n",
       "676   72.488981                     0.304051          -0.001854   \n",
       "677  -12.489566                    -0.293594          -0.014073   \n",
       "\n",
       "     three_month_CD_rate  Unemployment_rate  \n",
       "0               0.028146           -0.84438  \n",
       "1              -0.061854            0.25562  \n",
       "2               0.001489           -0.09635  \n",
       "3              -0.037781            0.07781  \n",
       "4              -0.030365           -0.11854  \n",
       "..                   ...                ...  \n",
       "673             0.028146            0.25927  \n",
       "674            -0.011854           -0.27781  \n",
       "675            -0.008146            0.23708  \n",
       "676             0.020000           -0.43708  \n",
       "677            -0.001854            0.05562  \n",
       "\n",
       "[676 rows x 5 columns]"
      ]
     },
     "execution_count": 517,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 284,
   "id": "c464250e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# the dependent and independent variable should be linearly related\n",
    "#Now I'll go back to regression equation only with ytminus1 as x variable and take out its fitted values\n",
    "#take their square and add that variable as x and regress again with additional x variables - ytminus1 and fittedsquare"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 472,
   "id": "f309faa4",
   "metadata": {},
   "outputs": [],
   "source": [
    "forecasted_y_5_1 = model5_1.fittedvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 551,
   "id": "ed5ae0bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Actual vs Predicted S&P')"
      ]
     },
     "execution_count": 551,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(transformed_y3_2,forecasted_y_5_1)\n",
    "plt.xlabel('Actual')\n",
    "plt.ylabel('Predicted')\n",
    "plt.title('Actual vs Predicted S&P')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 552,
   "id": "3e9e3386",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept            0.965131\n",
       "transformed_IPI      0.000144\n",
       "transformed_tbill    0.002452\n",
       "transformed_cd       0.000973\n",
       "transformed_un       0.000516\n",
       "dtype: float64"
      ]
     },
     "execution_count": 552,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model5_1.pvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c3800d81",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Since the plots are not scattered around a 45 degree line, there is a problem of linear relationship in our data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "921f2e6c",
   "metadata": {},
   "outputs": [],
   "source": [
    "#df10_2 is the final dataframe to be worked on"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea3e9dc1",
   "metadata": {},
   "source": [
    "### Polynomial regression for correcting Non Linear relationship"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 518,
   "id": "c477c283",
   "metadata": {},
   "outputs": [],
   "source": [
    "Industrial_Production_Index2 = df12['Industrial_Production_Index'] ** 2\n",
    "three_Month_Tbill2 = df12['three_Month_Tbill'] ** 2\n",
    "three_month_CD_rate2 = df12['three_month_CD_rate'] ** 2\n",
    "Unemployment_rate2 = df12['Unemployment_rate'] ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 519,
   "id": "36a5c12e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SandP</th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.774015</td>\n",
       "      <td>0.303977</td>\n",
       "      <td>-0.168876</td>\n",
       "      <td>0.028146</td>\n",
       "      <td>-0.84438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.835985</td>\n",
       "      <td>-0.182023</td>\n",
       "      <td>-0.048876</td>\n",
       "      <td>-0.061854</td>\n",
       "      <td>0.25562</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.601738</td>\n",
       "      <td>-0.001971</td>\n",
       "      <td>-0.040000</td>\n",
       "      <td>0.001489</td>\n",
       "      <td>-0.09635</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-5.480759</td>\n",
       "      <td>0.044988</td>\n",
       "      <td>-0.066292</td>\n",
       "      <td>-0.037781</td>\n",
       "      <td>0.07781</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.849485</td>\n",
       "      <td>0.053407</td>\n",
       "      <td>0.109635</td>\n",
       "      <td>-0.030365</td>\n",
       "      <td>-0.11854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>673</th>\n",
       "      <td>178.093020</td>\n",
       "      <td>-0.344435</td>\n",
       "      <td>0.012219</td>\n",
       "      <td>0.028146</td>\n",
       "      <td>0.25927</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>674</th>\n",
       "      <td>-121.077793</td>\n",
       "      <td>-0.546488</td>\n",
       "      <td>0.010000</td>\n",
       "      <td>-0.011854</td>\n",
       "      <td>-0.27781</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>675</th>\n",
       "      <td>-39.119200</td>\n",
       "      <td>0.094830</td>\n",
       "      <td>0.024073</td>\n",
       "      <td>-0.008146</td>\n",
       "      <td>0.23708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>676</th>\n",
       "      <td>72.488981</td>\n",
       "      <td>0.304051</td>\n",
       "      <td>-0.001854</td>\n",
       "      <td>0.020000</td>\n",
       "      <td>-0.43708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>677</th>\n",
       "      <td>-12.489566</td>\n",
       "      <td>-0.293594</td>\n",
       "      <td>-0.014073</td>\n",
       "      <td>-0.001854</td>\n",
       "      <td>0.05562</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>676 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          SandP  Industrial_Production_Index  three_Month_Tbill  \\\n",
       "0     -0.774015                     0.303977          -0.168876   \n",
       "1      0.835985                    -0.182023          -0.048876   \n",
       "2      0.601738                    -0.001971          -0.040000   \n",
       "3     -5.480759                     0.044988          -0.066292   \n",
       "4      1.849485                     0.053407           0.109635   \n",
       "..          ...                          ...                ...   \n",
       "673  178.093020                    -0.344435           0.012219   \n",
       "674 -121.077793                    -0.546488           0.010000   \n",
       "675  -39.119200                     0.094830           0.024073   \n",
       "676   72.488981                     0.304051          -0.001854   \n",
       "677  -12.489566                    -0.293594          -0.014073   \n",
       "\n",
       "     three_month_CD_rate  Unemployment_rate  \n",
       "0               0.028146           -0.84438  \n",
       "1              -0.061854            0.25562  \n",
       "2               0.001489           -0.09635  \n",
       "3              -0.037781            0.07781  \n",
       "4              -0.030365           -0.11854  \n",
       "..                   ...                ...  \n",
       "673             0.028146            0.25927  \n",
       "674            -0.011854           -0.27781  \n",
       "675            -0.008146            0.23708  \n",
       "676             0.020000           -0.43708  \n",
       "677            -0.001854            0.05562  \n",
       "\n",
       "[676 rows x 5 columns]"
      ]
     },
     "execution_count": 519,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df13 = df12 + 0\n",
    "\n",
    "cols8 = df13.columns\n",
    "df13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 520,
   "id": "077bc503",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "x8 = cols8[1:]\n",
    "y8 = cols8[0:1]\n",
    "y8 = df13[y8]\n",
    "x8 = df13[x8]\n",
    "\n",
    "x8.loc[:,'Industrial_Production_Index2'] = Industrial_Production_Index2\n",
    "x8.loc[:,'three_Month_Tbill2'] = three_Month_Tbill2\n",
    "x8.loc[:,'three_month_CD_rate2'] = three_month_CD_rate2\n",
    "x8.loc[:,'Unemployment_rate2'] = Unemployment_rate2\n",
    "\n",
    "\n",
    "df13 = pd.concat([y8,x8],axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 521,
   "id": "60316a37",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SandP</th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "      <th>Industrial_Production_Index2</th>\n",
       "      <th>three_Month_Tbill2</th>\n",
       "      <th>three_month_CD_rate2</th>\n",
       "      <th>Unemployment_rate2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.774015</td>\n",
       "      <td>0.303977</td>\n",
       "      <td>-0.168876</td>\n",
       "      <td>0.028146</td>\n",
       "      <td>-0.84438</td>\n",
       "      <td>0.092402</td>\n",
       "      <td>0.028519</td>\n",
       "      <td>0.000792</td>\n",
       "      <td>0.712978</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.835985</td>\n",
       "      <td>-0.182023</td>\n",
       "      <td>-0.048876</td>\n",
       "      <td>-0.061854</td>\n",
       "      <td>0.25562</td>\n",
       "      <td>0.033132</td>\n",
       "      <td>0.002389</td>\n",
       "      <td>0.003826</td>\n",
       "      <td>0.065342</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.601738</td>\n",
       "      <td>-0.001971</td>\n",
       "      <td>-0.040000</td>\n",
       "      <td>0.001489</td>\n",
       "      <td>-0.09635</td>\n",
       "      <td>0.000004</td>\n",
       "      <td>0.001600</td>\n",
       "      <td>0.000002</td>\n",
       "      <td>0.009283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-5.480759</td>\n",
       "      <td>0.044988</td>\n",
       "      <td>-0.066292</td>\n",
       "      <td>-0.037781</td>\n",
       "      <td>0.07781</td>\n",
       "      <td>0.002024</td>\n",
       "      <td>0.004395</td>\n",
       "      <td>0.001427</td>\n",
       "      <td>0.006054</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.849485</td>\n",
       "      <td>0.053407</td>\n",
       "      <td>0.109635</td>\n",
       "      <td>-0.030365</td>\n",
       "      <td>-0.11854</td>\n",
       "      <td>0.002852</td>\n",
       "      <td>0.012020</td>\n",
       "      <td>0.000922</td>\n",
       "      <td>0.014052</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      SandP  Industrial_Production_Index  three_Month_Tbill  \\\n",
       "0 -0.774015                     0.303977          -0.168876   \n",
       "1  0.835985                    -0.182023          -0.048876   \n",
       "2  0.601738                    -0.001971          -0.040000   \n",
       "3 -5.480759                     0.044988          -0.066292   \n",
       "4  1.849485                     0.053407           0.109635   \n",
       "\n",
       "   three_month_CD_rate  Unemployment_rate  Industrial_Production_Index2  \\\n",
       "0             0.028146           -0.84438                      0.092402   \n",
       "1            -0.061854            0.25562                      0.033132   \n",
       "2             0.001489           -0.09635                      0.000004   \n",
       "3            -0.037781            0.07781                      0.002024   \n",
       "4            -0.030365           -0.11854                      0.002852   \n",
       "\n",
       "   three_Month_Tbill2  three_month_CD_rate2  Unemployment_rate2  \n",
       "0            0.028519              0.000792            0.712978  \n",
       "1            0.002389              0.003826            0.065342  \n",
       "2            0.001600              0.000002            0.009283  \n",
       "3            0.004395              0.001427            0.006054  \n",
       "4            0.012020              0.000922            0.014052  "
      ]
     },
     "execution_count": 521,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df13.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 522,
   "id": "bf23ff98",
   "metadata": {},
   "outputs": [],
   "source": [
    "model9 = ols('SandP ~ Industrial_Production_Index + three_Month_Tbill + three_month_CD_rate + Unemployment_rate + Industrial_Production_Index2 + three_Month_Tbill2 + three_month_CD_rate2 + Unemployment_rate2',df13).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 523,
   "id": "b1b532c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept                       0.776631\n",
       "Industrial_Production_Index     0.001453\n",
       "three_Month_Tbill               0.002839\n",
       "three_month_CD_rate             0.001360\n",
       "Unemployment_rate               0.003718\n",
       "Industrial_Production_Index2    0.176981\n",
       "three_Month_Tbill2              0.931680\n",
       "three_month_CD_rate2            0.904446\n",
       "Unemployment_rate2              0.429704\n",
       "dtype: float64"
      ]
     },
     "execution_count": 523,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model9.pvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 524,
   "id": "68a9f67b",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "p_value5 = list(model9.pvalues)\n",
    "df14 = df13 + 0\n",
    "cols9 = df14.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 525,
   "id": "0dd8cbd3",
   "metadata": {},
   "outputs": [],
   "source": [
    "max_value5 = cols9[p_value5.index(max(p_value5[1:]))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 526,
   "id": "87cda74f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Drop the variable three_Month_Tbill2\n"
     ]
    }
   ],
   "source": [
    "if max(p_value5[1:]) > 0.05:\n",
    "    max_value5 = cols9[p_value5.index(max(p_value5[1:]))]\n",
    "    print('Drop the variable ' + str(max_value5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 527,
   "id": "b7e018e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "df15 = df14.drop(columns=['three_Month_Tbill2'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 531,
   "id": "4d09a211",
   "metadata": {},
   "outputs": [],
   "source": [
    "model10 = ols('SandP ~ Industrial_Production_Index + three_Month_Tbill + three_month_CD_rate + Unemployment_rate + Industrial_Production_Index2 + three_month_CD_rate2 + Unemployment_rate2',df15).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 532,
   "id": "b505fe89",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept                       0.781205\n",
       "Industrial_Production_Index     0.001445\n",
       "three_Month_Tbill               0.002799\n",
       "three_month_CD_rate             0.001175\n",
       "Unemployment_rate               0.003652\n",
       "Industrial_Production_Index2    0.177107\n",
       "three_month_CD_rate2            0.677065\n",
       "Unemployment_rate2              0.430871\n",
       "dtype: float64"
      ]
     },
     "execution_count": 532,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model10.pvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 533,
   "id": "4778e8d1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Drop the variable three_month_CD_rate2\n"
     ]
    }
   ],
   "source": [
    "p_value6 = list(model10.pvalues)\n",
    "df16 = df15 + 0\n",
    "cols10 = df16.columns\n",
    "\n",
    "if max(p_value6[1:]) > 0.05:\n",
    "    max_value6 = cols10[p_value6.index(max(p_value6[1:]))]\n",
    "    print('Drop the variable ' + str(max_value6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 535,
   "id": "8410e400",
   "metadata": {},
   "outputs": [],
   "source": [
    "df16_1 = df16.drop(columns=['three_month_CD_rate2'])\n",
    "\n",
    "model11 = ols('SandP ~ Industrial_Production_Index + three_Month_Tbill + three_month_CD_rate + Unemployment_rate + Industrial_Production_Index2 + Unemployment_rate2',df16_1).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 536,
   "id": "47ca45a0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Drop the variable Unemployment_rate2\n"
     ]
    }
   ],
   "source": [
    "p_value7 = list(model11.pvalues)\n",
    "df17 = df16_1 + 0\n",
    "cols11 = df17.columns\n",
    "\n",
    "if max(p_value7[1:]) > 0.05:\n",
    "    max_value7 = cols11[p_value7.index(max(p_value7[1:]))]\n",
    "    print('Drop the variable ' + str(max_value7))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 538,
   "id": "93c340cd",
   "metadata": {},
   "outputs": [],
   "source": [
    "df17_1 = df17.drop(columns=['Unemployment_rate2'])\n",
    "\n",
    "model12 = ols('SandP ~ Industrial_Production_Index + three_Month_Tbill + three_month_CD_rate + Unemployment_rate + Industrial_Production_Index2',df17_1).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 540,
   "id": "ca101233",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept                       0.911604\n",
       "Industrial_Production_Index     0.001060\n",
       "three_Month_Tbill               0.002359\n",
       "three_month_CD_rate             0.000772\n",
       "Unemployment_rate               0.002148\n",
       "Industrial_Production_Index2    0.189630\n",
       "dtype: float64"
      ]
     },
     "execution_count": 540,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model12.pvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a39cdb4d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 542,
   "id": "d8ecc9a6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Drop the variable Industrial_Production_Index2\n"
     ]
    }
   ],
   "source": [
    "p_value8 = list(model12.pvalues)\n",
    "df18 = df17_1 + 0\n",
    "cols12 = df18.columns\n",
    "\n",
    "if max(p_value8[1:]) > 0.05:\n",
    "    max_value8 = cols12[p_value8.index(max(p_value8[1:]))]\n",
    "    print('Drop the variable ' + str(max_value8))\n",
    "else:\n",
    "    print('No valriable to be dropped')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 544,
   "id": "834adf37",
   "metadata": {},
   "outputs": [],
   "source": [
    "df19 = df18.drop(columns=['Industrial_Production_Index2'])\n",
    "\n",
    "model12_1 = ols('SandP ~ Industrial_Production_Index + three_Month_Tbill + three_month_CD_rate + Unemployment_rate',df19).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 545,
   "id": "840ea454",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept                      0.965131\n",
       "Industrial_Production_Index    0.000144\n",
       "three_Month_Tbill              0.002452\n",
       "three_month_CD_rate            0.000973\n",
       "Unemployment_rate              0.000516\n",
       "dtype: float64"
      ]
     },
     "execution_count": 545,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model12_1.pvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cff5dbb4",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 546,
   "id": "432f61fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SandP</th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.774015</td>\n",
       "      <td>0.303977</td>\n",
       "      <td>-0.168876</td>\n",
       "      <td>0.028146</td>\n",
       "      <td>-0.84438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.835985</td>\n",
       "      <td>-0.182023</td>\n",
       "      <td>-0.048876</td>\n",
       "      <td>-0.061854</td>\n",
       "      <td>0.25562</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.601738</td>\n",
       "      <td>-0.001971</td>\n",
       "      <td>-0.040000</td>\n",
       "      <td>0.001489</td>\n",
       "      <td>-0.09635</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-5.480759</td>\n",
       "      <td>0.044988</td>\n",
       "      <td>-0.066292</td>\n",
       "      <td>-0.037781</td>\n",
       "      <td>0.07781</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.849485</td>\n",
       "      <td>0.053407</td>\n",
       "      <td>0.109635</td>\n",
       "      <td>-0.030365</td>\n",
       "      <td>-0.11854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>673</th>\n",
       "      <td>178.093020</td>\n",
       "      <td>-0.344435</td>\n",
       "      <td>0.012219</td>\n",
       "      <td>0.028146</td>\n",
       "      <td>0.25927</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>674</th>\n",
       "      <td>-121.077793</td>\n",
       "      <td>-0.546488</td>\n",
       "      <td>0.010000</td>\n",
       "      <td>-0.011854</td>\n",
       "      <td>-0.27781</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>675</th>\n",
       "      <td>-39.119200</td>\n",
       "      <td>0.094830</td>\n",
       "      <td>0.024073</td>\n",
       "      <td>-0.008146</td>\n",
       "      <td>0.23708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>676</th>\n",
       "      <td>72.488981</td>\n",
       "      <td>0.304051</td>\n",
       "      <td>-0.001854</td>\n",
       "      <td>0.020000</td>\n",
       "      <td>-0.43708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>677</th>\n",
       "      <td>-12.489566</td>\n",
       "      <td>-0.293594</td>\n",
       "      <td>-0.014073</td>\n",
       "      <td>-0.001854</td>\n",
       "      <td>0.05562</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>676 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          SandP  Industrial_Production_Index  three_Month_Tbill  \\\n",
       "0     -0.774015                     0.303977          -0.168876   \n",
       "1      0.835985                    -0.182023          -0.048876   \n",
       "2      0.601738                    -0.001971          -0.040000   \n",
       "3     -5.480759                     0.044988          -0.066292   \n",
       "4      1.849485                     0.053407           0.109635   \n",
       "..          ...                          ...                ...   \n",
       "673  178.093020                    -0.344435           0.012219   \n",
       "674 -121.077793                    -0.546488           0.010000   \n",
       "675  -39.119200                     0.094830           0.024073   \n",
       "676   72.488981                     0.304051          -0.001854   \n",
       "677  -12.489566                    -0.293594          -0.014073   \n",
       "\n",
       "     three_month_CD_rate  Unemployment_rate  \n",
       "0               0.028146           -0.84438  \n",
       "1              -0.061854            0.25562  \n",
       "2               0.001489           -0.09635  \n",
       "3              -0.037781            0.07781  \n",
       "4              -0.030365           -0.11854  \n",
       "..                   ...                ...  \n",
       "673             0.028146            0.25927  \n",
       "674            -0.011854           -0.27781  \n",
       "675            -0.008146            0.23708  \n",
       "676             0.020000           -0.43708  \n",
       "677            -0.001854            0.05562  \n",
       "\n",
       "[676 rows x 5 columns]"
      ]
     },
     "execution_count": 546,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df19"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "39c228c0",
   "metadata": {},
   "outputs": [],
   "source": [
    "#now we can see that there is no variable to drop anymore"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 547,
   "id": "42809fa0",
   "metadata": {},
   "outputs": [],
   "source": [
    "fitted_model12_1 = model12_1.fittedvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 548,
   "id": "0a38fcb7",
   "metadata": {},
   "outputs": [],
   "source": [
    "df19.loc[:,'fitted model12_1'] = fitted_model12_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 550,
   "id": "45e9757f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Actual vs Predicted S&P')"
      ]
     },
     "execution_count": 550,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(df19.SandP,fitted_model12_1)\n",
    "\n",
    "plt.xlabel('Actual')\n",
    "plt.ylabel('Predicted')\n",
    "plt.title('Actual vs Predicted S&P')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c80818f0",
   "metadata": {},
   "source": [
    "### Hateroskedasticity check - Breusch pagan test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 563,
   "id": "c591d43c",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Error terms should have a constant variance\n",
    "#If chi sq statistic is less than chi sq critical, then there is no problem of hateroskedasticity\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 571,
   "id": "6a93587d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('Lagrange multiplier statistic', 2.750923557231835),\n",
       " ('p-value', 0.6003335107599259),\n",
       " ('f-value', 0.6854334344784908),\n",
       " ('f p-value', 0.6021950567555951)]"
      ]
     },
     "execution_count": 571,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names = ['Lagrange multiplier statistic', 'p-value','f-value', 'f p-value']\n",
    "test = sms.het_breuschpagan(model12_1.resid, model12_1.model.exog)\n",
    "lzip(names, test)\n",
    "\n",
    "#https://www.statology.org/breusch-pagan-test-python/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 559,
   "id": "f70c2444",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SandP</th>\n",
       "      <th>Industrial_Production_Index</th>\n",
       "      <th>three_Month_Tbill</th>\n",
       "      <th>three_month_CD_rate</th>\n",
       "      <th>Unemployment_rate</th>\n",
       "      <th>fitted model12_1</th>\n",
       "      <th>error2sq</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.774015</td>\n",
       "      <td>0.303977</td>\n",
       "      <td>-0.168876</td>\n",
       "      <td>0.028146</td>\n",
       "      <td>-0.84438</td>\n",
       "      <td>5.964109</td>\n",
       "      <td>45.402314</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.835985</td>\n",
       "      <td>-0.182023</td>\n",
       "      <td>-0.048876</td>\n",
       "      <td>-0.061854</td>\n",
       "      <td>0.25562</td>\n",
       "      <td>-1.960894</td>\n",
       "      <td>7.822532</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.601738</td>\n",
       "      <td>-0.001971</td>\n",
       "      <td>-0.040000</td>\n",
       "      <td>0.001489</td>\n",
       "      <td>-0.09635</td>\n",
       "      <td>0.634784</td>\n",
       "      <td>0.001092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-5.480759</td>\n",
       "      <td>0.044988</td>\n",
       "      <td>-0.066292</td>\n",
       "      <td>-0.037781</td>\n",
       "      <td>0.07781</td>\n",
       "      <td>-2.233847</td>\n",
       "      <td>10.542439</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.849485</td>\n",
       "      <td>0.053407</td>\n",
       "      <td>0.109635</td>\n",
       "      <td>-0.030365</td>\n",
       "      <td>-0.11854</td>\n",
       "      <td>3.583520</td>\n",
       "      <td>3.006876</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      SandP  Industrial_Production_Index  three_Month_Tbill  \\\n",
       "0 -0.774015                     0.303977          -0.168876   \n",
       "1  0.835985                    -0.182023          -0.048876   \n",
       "2  0.601738                    -0.001971          -0.040000   \n",
       "3 -5.480759                     0.044988          -0.066292   \n",
       "4  1.849485                     0.053407           0.109635   \n",
       "\n",
       "   three_month_CD_rate  Unemployment_rate  fitted model12_1   error2sq  \n",
       "0             0.028146           -0.84438          5.964109  45.402314  \n",
       "1            -0.061854            0.25562         -1.960894   7.822532  \n",
       "2             0.001489           -0.09635          0.634784   0.001092  \n",
       "3            -0.037781            0.07781         -2.233847  10.542439  \n",
       "4            -0.030365           -0.11854          3.583520   3.006876  "
      ]
     },
     "execution_count": 559,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "error2 = model12_1.resid\n",
    "error2sq = model12_1.resid ** 2\n",
    "\n",
    "df20 = df19 + 0\n",
    "df20.loc[:,'error2sq'] = error2sq\n",
    "df20.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 554,
   "id": "5c407709",
   "metadata": {},
   "outputs": [],
   "source": [
    "model13 = ols('error2sq ~ Industrial_Production_Index + three_Month_Tbill + three_month_CD_rate + Unemployment_rate',df20).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 555,
   "id": "23f28f87",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "676"
      ]
     },
     "execution_count": 555,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df20.SandP.count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 556,
   "id": "6deb2cb2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.750923557231835"
      ]
     },
     "execution_count": 556,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chi_sq_stats = df20.SandP.count()*model13.rsquared\n",
    "chi_sq_stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 560,
   "id": "ad745f38",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.8414588206941285"
      ]
     },
     "execution_count": 560,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chi_critical = chi2.isf(q=0.05, df = 1)\n",
    "chi_critical"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "07abea51",
   "metadata": {},
   "outputs": [],
   "source": [
    "#since chi_sq_stats is less than chi_critical, out model is not hateroskedastic, our model is fine"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d3fa4bbd",
   "metadata": {},
   "source": [
    "### Error terms should be normally distributed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 572,
   "id": "457b8b39",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(error2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8d5bc9cd",
   "metadata": {},
   "source": [
    "### Principal Component Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8755bb7c",
   "metadata": {},
   "outputs": [],
   "source": [
    "cols_1 = df.columns\n",
    "\n",
    "y_1 = cols[1]\n",
    "y_1 = df[y_1]\n",
    "x_1 = cols[2:11]\n",
    "x_1 = df[x_1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "30eab09a",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_std = StandardScaler().fit_transform(x_1)\n",
    "pca = PCA().fit(X_std)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "52b1dbec",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.cumsum(pca.explained_variance_ratio_)\n",
    "#cumulative contributions - obviously this will add up to 1 in the end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5f870022",
   "metadata": {},
   "outputs": [],
   "source": [
    "pca.explained_variance_ratio_\n",
    "#individual contributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "89aedfc9",
   "metadata": {},
   "outputs": [],
   "source": [
    "pca = PCA(n_components=5)\n",
    "X_pca = pca.fit_transform(X_std)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "734f73b9",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_pca_with_constant = sm.add_constant(X_pca)\n",
    "model14 = sm.OLS(y_1,X_pca_with_constant)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4b85655a",
   "metadata": {},
   "outputs": [],
   "source": [
    "results14 = model14.fit()\n",
    "print(results14.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5208be54",
   "metadata": {},
   "outputs": [],
   "source": [
    "#https://www.youtube.com/watch?v=7A6vukBvooE\n",
    "#https://github.com/bhattbhavesh91/pca-multicollinearity/blob/master/multi-collinearity-pca-notebook.ipynb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "16255b94",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8d73ac5c",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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