13a_Random_Variables.ipynb

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   "source": [
    "(chap:13a-random)=\n",
    "# ランダム変数と統計的特徴"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div name=\"html-admonition\" style=\"font-size: 0.8em\">\n",
    "<input type=\"button\" onclick=\"location.href='https://translate.google.com/translate?hl=&sl=ja&tl=en&u='+window.location;\" value=\"Google translation\" style=\"color:#ffffff;background-color:#008080; height:25px\" onmouseover=\"this.style.background='#99ccff'\" onmouseout=\"this.style.background='#008080'\"/> in English or the language of your choice.\n",
    "</div><br>"
   ]
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  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "import japanize_matplotlib\n",
    "import py4macro\n",
    "\n",
    "# numpy v1の表示を使用\n",
    "np.set_printoptions(legacy='1.21')\n",
    "# 警告メッセージを非表示\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "## はじめに"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "この章以降では短期的なマクロ経済分析について議論し、特に、景気循環の発生メカニズムの理解が大きな目的である。\n",
    "本章は、その最初の章であり、分析の大前提となるランダム変数について説明し、マクロ経済分析において重要となる統計的な特徴について復習する。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "GDPや消費などのマクロ変数は右上がりの長期的なトレンドがある。\n",
    "また、失業率やインフレ率に関しても長期的なトレンドを考えることもできる。\n",
    "トレンドの詳細については後に議論するとして、トレンドの周りをマクロ変数が変動し、それが景気循環だと解釈できる。\n",
    "下の図では、日本のGDPの長期的トレンドからの乖離をパーセントで表している。\n",
    "波打つように上下に、時には小刻みに、また時には大きく乱高下しているように見える。"
   ]
  },
  {
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   "execution_count": 10,
   "metadata": {
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    "hidden": true,
    "slideshow": {
     "slide_type": ""
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    "tags": [
     "hide-input"
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   "outputs": [
    {
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SQUhdXR127doV8+tnz56NoUOHhl3ugw8+wOuvvw4AuPvuu0MaHkXC008/jSFDhuD2228PGYSEQ6fT4ZtvvkFzczP27duHRYsW4aGHHkJjYyMA2XypoKAAer0eVVVVeOmll5CXl4euri58+umnYj1ZWVn497//DUmS8N133+HFF1+M6P23bNkCAJg4cWLM+xCK/fv34x//+Ad0Oh1efPFFv8ADkM8NVqsV+fn5GDFiRNB1/eY3v4EkSaivr4/qxmHnzp1YtWpVyN+O1WrFqlWrsGnTpojXy5k2bRruuecerF+/HieccAIGDhyI7777DosWLRLBxlNPPYWGhgZcfPHFAIDu7m40NjaisbFRnBdbWlrEY2r/Ph0OB/bu3QsAGDlyZNjlJUnCb3/7WwCyOeGOHTsAAB0dHbj++uvBGMMJJ5yAIUOGAAAeeOABbN26FWeeeSbOPPNMVbZ51KhRAOTjRyCO2nWaw9vJALD33ntPlXXGknZhzGN+A7dkGu06e3p62C9+8Qux3PLly/2WOfXUU8NKxDxv+uc//znk9nIJFABbt25dmL3zRpl24VIp3KmvBx98kHV2dka1vkDEmnbp7OxkU6dOZbNnz465UyMS6uvrWb9+/RgANmPGjICyfyQo0y68wBAAy8rKYrfddltMHS2BWLNmjVhvoONzwgknMADs3nvv9XvuN7/5DQPk7rBIPGhGjx7NALBPPvnE63GLxcI+/vhjdsMNN7BTTjmFTZkyhU2ZMoX96le/Yo899ljEnRiPPPIIA0IbTT311FMMADv++OPDro+broUqwvXlV7/6FQPAvvvuO8ZY4LQLP7aTJk3yem1ra2tQ8zyedonk74QTTmDDhw9nX375ZUTLK1tx1YDvM4CIO5e6urpErY3RaGSTJk1i+fn5DJAtEvi5c/PmzcxkMrG8vLyImggihbfczps3T7V1ahmyV48R5ewANSS53pCTkyP+v62tLaLXdHd3Y//+/fjmm2/w+OOPY/v27QCAyy+/HEcccYTXsjabDV999RUAYN68eQHXZ7PZ8MUXXwAATjjhhJDvrbTorq2tjfku9eeff8abb76Ju+++G3v27MFdd92FJ554Ag8//HBMcnNvcLlcuOCCC4R8+9NPP8VFEbNYLPjVr36FQ4cOwWw24+WXXw549x0tb7zxBvbs2YPbb78dq1atwiOPPILnn38e9957L2666SYYjcaY1/3KK68AAH71q18FVGh4ii7Qd/fBBx/Eu+++i9bWVvzlL3/B448/HvR9GGPYs2cPAGDYsGFinY8++iieeOIJr7QOZ82aNfjwww9x77334vnnn8eFF14Ycl8+/vhjAMF/BwCwaNEiAOF/B4D8Wzhw4ABqa2v9ntu1axfOO++8gI/HwldffYXLL78cdXV1eOONN3DOOed4PT9nzhwYDJ5LwqZNm/DRRx/hhBNOwLRp07yWvf7661FXV4eenh4AwMyZMzFr1iwAwOeff461a9fimmuuQX5+PgCobuvO39doNHptcyiysrKwZMkSXHvttXjvvfdE2mrGjBl45plnMH78eDDG8Nvf/hY2mw2PP/44KioqAMhzY/785z9jxYoVcDqdOOKII3Dfffdh5syZEW8z/+53d3dHs6vpS7KjH63ywQcfiMg7XKfB9ddfH/SOQFmUFavy8dhjj4nXrVy50uu5YPbqvn86nY7ddNNNAe8i9u7dK5YJdpf9+eefM0Du9w9319/a2ire94svvohqXwMVnHZ3d7P/+7//E8WXANjRRx8tjJGiJVrlw+l0smuuuUa89+233x7T+4bD5XKxefPmifd59tlne7W+QAWnTqeTPfvss16eFGPGjInZat7hcAiV5vPPPw+4zHnnnccAsNtuuy3g83fffTcD5A6WUD46NTU14ntqtVrZ66+/LvYjLy+PXX/99ezzzz9nhw4dYlarle3du5e9//77oj0cAHv33XdD7g9vOw5WLN3e3i58bTZt2hRyXYwxNnnyZAaA3X333X7Pbd++PWCXSk5OTlTKx6pVq8R3GpBN4n788cew2/bggw+GVXb57zHRBaf19fVif2JR/hobG9maNWv8PD+effZZBsieO9z076233hI2ATqdTni6GAyGsN8XJVwRO/vss6Pe3nSEgo8YWbZsmfjyh2tBvPPOO72szXmVu1rBx1133SVe5/tjCmav3r9/fzZy5Eh28skns/vvvz+k++hPP/3EANnMLBjc7OfKK68Mu70bN24U2xStF0Oobpdt27axo446SjxvMBjYzTffHHWlejTBR1dXFzvjjDPEe1566aVxcSq1Wq1eTrS///3ve73OUN0u9fX17JxzzvEKUOfNm+dnjBeO999/nwGy4VSwz4WnEQKlXRiTLxT5+fnsL3/5S8jA9rvvvhMBMG+RNBgM7Pbbbw85t8PlconPdsiQISHfg/vqbN26NeDzL774IgPAhg8fHnQdSri3zuOPPx7R8oxFl3ZRjneYMmVK0Ivltm3b2EUXXeT1N2rUKAaAzZ071+85nkZJVvBhs9lEQKCWeVldXR3Lz89nRqNRzKSpra0Vwd7vfvc71tnZydrb29mNN94ogtpI05O8O+i3v/2tKturdSj4iJH29nZmMBgivuAqCXbSjzX4mDNnjggufIl1nUp4sFBUVBTw+fr6enG3F6hexJcnn3ySAWAZGRlR23SHa7V1Op3skUceEdtjNBqjVkAiDT4OHDjApk+fLrbniiuuiEvg0dLSwo477jjxPhdccIEq7xNJq+2bb77ppYJEq4Acc8wxDAhtS33EEUcwIHTdQygzLg53ouR/gwcPjugOnzF5NhN/3bZt24Iux907g32nuJLha1YViPXr14v3/OabbyLaTsaiCz4MBgM766yzwh43HriZzWaWn58v5knp9Xrxb+Xj/fr1Y4wlL/hgzKNCqeUaymvW7rnnHvEY9zoZO3asV1DqcrlEfVGkrs38Bu1vf/ubKturdajbJUZyc3NFV8iiRYtgt9uTsh0tLS1Yvnw5AOD444+Py3sMHDgQer0ezc3NomtBydNPPw2bzYapU6f61Yv44nK58NJLLwEAjj76aGRkZKi6rTqdDrfeeitWrFiBUaNG4a677sKECRNUfQ8A+N///ofp06dj5cqVkCQJCxYswEsvvQSdTt2f1Oeff47x48djyZIlAIAbbrgBr732murvE4xzzz0Xa9euxdFHH43LL788qu/YunXr8O2338JoNOLyyy8Puhxv8eadBoEoLy8P+351dXXi/w8//HD89NNPEbVhAnJ7OEdZz+UL70TiNVJKlixZgrVr18JsNouOrlA8//zzAORzSbzGzo8bNw7vvvuu13FbtGgRPvjgA9E2q+SGG25Aa2srampqoNPpcPbZZ6O1tRVfffUVWltb0draioEDB/q97n//+x+uvPJKXHnllfj2228ByN1o/DHemaUmvJ2at9z2hkWLFuHdd9/FiBEj8Ic//EE8zn93l19+OSRJEo9LkoTLLrsMAPDNN99E9B58O+PZBq4pkh39aBmlE+O//vWviF+npvLx5z//Wbwm2mF10cDz4r77eejQISFLvvbaa2HXo6xP8e1IiIRoTMY6OztjchMMpXzU1NSIuR1wS/yBPvfesm/fPtHpAbeC8/DDD6v6HtGYjDkcjqg7iXgq4+KLLw66jLJrIVgqI1K+/vprdswxx7Cjjz46agv4b775RmxHKKtubpvua5PtcrlEx1AkSuiPP/4olNNIbeR/+OEHduWVVwpTwVi6XRjzdLU8//zz4jGufNx6662MMca++uorBoA9+eST7MMPP2SAp7Zt0KBBfspHuD+1u10Y89RQnHHGGb1aT3t7O6uqqmKAPNdGybBhwxgA9sEHH/i97p133mGAXBMVDl6PZDabWVdXV6+2N12g4KMX2Gw2YW1cUlISshhOyc6dO1UJPlauXCmKLGfNmhVwGbWCj5dfflnkspUXoTPPPFOc5MKlAl555RWRp/3FL34R03Yky+G0ra2N/e1vfxPTiwGw008/XbV2VM7WrVvZtddeK9JGgDy0z7eQWA2iCT6iZe3ataIwL9TU5ffee48BYGVlZaq+f7TwGSVjx44NudyuXbuYXq9nJpPJK/Xy97//nQFyO3G4upg1a9aIWo/y8vKgNQsul4v99NNP7N5772VjxoxhAEQaJNLgY+LEiX7r5QW+Sgt/3+Dj//7v/xggO5m6XC42fvx4Nm7cOOZyuQIGH8lIuxw4cIDp9XpmNptZc3NzzOu54YYbGAB2+eWX+z3Hz+//+9///J576623GCAPnAsHb9GmYlMPFHz0klWrVokAYNSoUWGtoJubm9ns2bPFyUJ58YomUFi0aJGYLVFUVBT0fdUKPux2O5s6dSoD5NHQy5YtY1dccYXIK4fKrdfU1HjdxY8YMYI1NTXFtB2JDj7279/PbrnlFjGTBpALb9966y1V3svpdLINGzawRx991Mu3BJCtxR944IGIrNZjIZ7BB/8M586dKx7jw8iU8KLWiy66SNX3jxSr1erVqRSJeseLDQcPHsw+//xz9thjjwkVI1ThaFdXF3vwwQfF+SIrKyvgDCTG5BoXPieJK19XXHEF27FjR0Q1H7W1tQwAy8zMZP/4xz/Ye++9x/773/+yO++8UwS2ymJvHnxcd911bPny5WzKlCksJyeHPfzww+zWW29l48aNYwDYl19+mTLBB2Oem5/HHnssptf/+OOPTKfTsbKysoDnpGOPPZYBgWf0PPDAAwwA++UvfxnyPZxOpyjejba7L52h4EMFFi1aJKrgs7Ky2N133802bNgg2lYdDgfbsGEDe+CBB1hxcTEDZNMk30FwoQIFh8PBduzYwRYuXCiCFwBswIABbNWqVUG3Ta3ggzH54qHs1AHkWQlK+ZbT1tbG3n33XXbRRRd53cUfffTRvapOT2TwUVJSIi4q/OR+xx13qDLngTE5ZcbvYpV/JSUl7M4774zIVKs3xCv4ULah//zzz+LxIUOGsPPOO499//33rKenh7399ttCCYtlzk9vsFgs7PXXXxcXBUDuZoiE7u5uv0CRB1C+nTJWq5V9++237Pe//71QOwCwysrKkIoQY4ydddZZbOjQoeyBBx7wSgVFEnw4HA5hYBbob9asWV7byoOPq6++2uv3ajAY2MSJE9nll1/OTCYTO//881Mq+Fi5cqU4D0YbpNvtdjZx4kQGgL3++usBl/nTn/4kFDFlS6/D4WBDhw5lQHiDuNdee40BspEf4YGCD5VYuXKlV+cDIPeE5+XlCfmZX6zPP//8gHnlYG2xyrtu5bovvfRSdvDgwZDbpWbwwRhjmzZtYnPmzGEZGRls3Lhxfh4nNTU1bMSIEV77zE8OL774Yq+7NBIRfChbZwHZX+Kqq66KeLhapOzcuVMErRkZGezkk09mr7/+esKmXsYj+LBYLCJ/7uvkWFZWFvBCeNRRR6ny3oGwWq2spaWF7d69m3311VfsqaeeYuecc45XEJ2VlcWefPLJqFxpW1pa2G9+8xuWm5vLysvL2V//+lev77bT6WQnn3yyV6srP8533nlnRAFsR0dHwG2KJPhgTB7y99JLL7H77ruP3XHHHWz+/PnsoYceYl988YWfN4Yy7bJw4UL29ttvs3Xr1nl1o918880pp3wwxthll13GALC77rorqtf99a9/ZQDYySefHHSZAwcOiJq23/zmN+zQoUOsvr6eXXrppeJGIVQbd1tbG6uoqGA6nS7izqu+AgUfKuJyudiiRYvY5ZdfzkaPHs0KCgqYwWBgxcXFbObMmeyee+4JWVQXzBCM53mHDx/OfvWrX7FHHnmE7du3L6JtUjv4iITbbrtNqDtnnHEGe+edd1S7oCYi+Dh48CA75phjWL9+/djdd9+tqsWyL4sWLWIff/xx3FIroYiX8vHpp5+yMWPG+AVrmzZtYpdeeqlX3czs2bPj9vk6HA4xfTbQX0FBAbv55psj/i1FCx/BYDab2ezZs9nTTz/dq9qEYKgx1da35sMXm83GGJPVgvz8/KgLTgHvibFq0tTUxKqqqpjBYIio1Z8xOfDPzMxk2dnZYb/7b7/9tpcCyv+MRmNYg0keGMXLeFDLUPBBqI7FYmHr1q2Li+dFIoIPxuQLFz/hpivxrPkIpSI4HA62b98+1Yt1A8E7IjIzM9mwYcPY6aefzv7v//6Pff311wk5vmvXrmUWiyWu75GI4GPs2LGsoqJCpI5GjRrFGPP8HouLiwO6sSr/1JqBFYgVK1awjIwMVllZGVYNZoyx448/ngFgjzzySETr/+GHH9jcuXNZcXExGzBgADvttNPCBjrPPfccA8COPfbYiOfP9CUo+CAIIm2x2+2svb092ZsRVxIRfMybN49lZGQwnU7HSktL2YsvvsgYC5x2SRYffPABMxgMbNKkSaylpSXocrxzb+rUqTEPZQzH+++/z/R6PZs8eXLItExfRmKMMRAEQRAEQSQIcjglCIIgCCKhUPBBEARBEERCoeCDIAiCIIiEQsEHQRAEQRAJxZDsDQiEy+VCXV0dcnNzvSYJEgRBEASRujDG0NHRgfLy8pDTt1My+Kirq0NVVVWyN4MgCIIgiBiorq5GZWVl0OdTMvjIzc0FIG98Xl5ekreGIAiCIIhIaG9vR1VVlbiOByMlgw+easnLy6PggyAIgiA0RriSCSo4JQiCIAgioVDwQRAEQRBEQqHggyAIgiCIhELBB0EQBEEQCYWCD4IgCIIgEgoFHwRBEARBJBQKPgiCIAiCSCgUfBAEQRAEkVAo+CAIgiAIIqFQ8EEQBEEQREKh4IMgCIIgiIRCwQdBEARBEAmFgg+CIIgks7O+A68s3wuXiyV7UwgiIaTkVFuCIIi+xJ3vbsCqfS0oyTHjlAkDkr05BBF3SPkgCIJIIha7E+uqWwEA62pak7otBJEoKPggCIJIIhtr2+Bwp1s217UneWsIIjFQ8EEQBJFEVu9vEf+/5UBHEreEIBIHBR8EQRBJZPW+VvH/jZ1W1HdYkrcxBJEgKPggCIJIEowxoXzodRIAUj+IvgEFHwRBEEmitrUH9R1WGHQSjh1ZCgDYcoDqPoj0h4IPgiCIJLFmfysAYMyAPEwdVAiAgg+ib0DBB0EQRJLgKZepAwswdkAeAOp4IfoGFHwQCcPmcOHc55fjvv9tSvamEERKsNqtfEwdVIix5XLwsbuxCxa7M4lbRRDxh4IPImFsP9SBn/Y04/Uf94MxspEm+g52p8vvMYvdic11bQCAKVWFKMs1oyjbBKeLYfshKjol0huyVycSRlOXDQBgc7rQ3GVDcY45yVtEEPGBMYZ7P9yE73c1oqHDig6LAxcfMRB/OWOCWGZjbRvsToaSHBOqijIhSRLGDMjF9zubsOVAOyZWFiRvBwgizpDyQSSMpk6r+P8DbeRlQKQve5u68eqKfdjd0IUOiwMA8OHaOi/Fj9d7TBlYCEmS22x53Qe12xLpDgUfRMJodisfAHConYIPIn3Z4U6bDC/Lwec3Hw2jXkKHxYGalh6xzLpqd8plYIF4bAwVnRJ9BAo+iITRpAg+SPkg0pmdDZ0AgHHleRjVPxcjynIBAJsVbbTra1sBAJMU6RVedLrlQDvVRRFpDQUfRMJo7vQEHwcp+CDSmJ31cvAxvDQHgCeo4IpGS5cN1c2yCjK+PF+8blhpDkx6HTqs3ioJQaQbFHwQCaOpy1PzcZDSLkQas4sHH2Vy8CHSKW7lY0OtnHIZXJyF/CyjeJ1Rr0P//AwAoBkvRFpDwQeRMJRpF1I+iHSFMYZdDV0APMGHr4HY+ppWAAjY0VKcYwIANCqUQoJINyj4IBKGsuCUlA8iXTnYbkGn1QG9TsKg4mwAnuCjtrUHbT12rK+RlY+Jlfl+ry/OloOPJgo+iDSGgg8iYVDNB9EX4PUeg4qzYDLIp9j8LCMqCjIByMWkPO0yoSJQ8CH73zQr0pQEkW6QyRiREKwOJzqsDvHvTqsDHRY7cjOMIV7Vd2CM4eut9dhc1466NvnO+dpjholCRUI7+BabcsaW56G2tQffbm/AgTYLJAkYFyj4oLQL0Qeg4INICDzlYtBJyDTq0WF14FC7xS/4eGX5Xjy5eAde/s1hGB/gxJyu/Ly3BVf8e6XXY0a9hMfOnZycDSJiZqdPsSln7IA8fLn5EN5ZVSM/X5qDHLP/KZg7/yprpAgi3aC0C5EQeP66MNuEAQVyNb+v10dtaw8e+HgLGjtt+HzTwYRvYzLZUS+bUg0qzsLJ4/oDoNSUVgkafLhVrIYOOZ0yIUC9B6Cs+aC0C5G+UPBBJASufBRnm9AvTw4+fC+uf/t0K6wOeQDXnsauxG5gkuGfxewRJfj1UYMAkAusVtnVEFz5UDIxiLLH0y7NpHwQaUxcgo9//etfGD9+PCoqKjB69Gg8++yz8XgbQkNwj4/iHBMG5PsHH6v2NeN/6+rEv/ta8MFVoAH5mSI4q++gO1+t0dptE7Uaw3xqPioLM5Gb4UmzTAgyOI4XnFLNB5HOqF7z8eqrr+KPf/wjPvvsM4wbNw5bt27FnDlzkJeXh4suukjttyM0Ak+7FGWb0T9frvo/4L6zd7kY/vTRFgDAYYOL8NPeZuxt7AJjTAzcSnd4INY/LwNlufLFp8PiQI/NiUyTPpmbRkQBT7mU52cg26eeQ5IkjB2Qhx/3NEOvk/yUEI5H+bDC5WLQ6frGb4DoW6iufKxYsQIPPfQQxo0bBwAYPXo0LrjgArz77rtqvxWhIZRpl/7uO/tD7gvupxsPYl11K7JNejx+/mToJKDL5hS58b7AgTbZSntAQQZyzAZkuQMOcrnUFjz4GOaTcuFwp9OR/XKDBpWFWXLw4WJAa489DltJEMlH9eDjmWeewQUXXOD12IYNG5CXF7xl0Gq1or293euPSC+UwQdPu/BUw4drawEAl80cjIqCTFQUyspIX0m9MMa80i6SJAn141B73wnA0oFgxaacE8f2AwBRVBwIk0GH/Ey5C4y8PvoWHRY7FnyyBRvcJnTpTFwLTu12O2688UYsX74ct912W9DlFixYgPz8fPFXVVUVz80ikgDPXxflmMTsikPtFljsTny3oxEAMHf8AADAkBL5xL23qW8EH+0WB7ptTgAQqlBZLs330CI7gxSbcmYOL8Hae0/EDXOGh1wP73ihuo++xdNLduL5pbvx1Nc7kr0pcSduwce+ffswe/ZsLF68GMuWLcP48eODLjt//ny0tbWJv+rq6nhtFpEk+B2cMu3S1GXDN9sa0GN3YkB+Bsa5WxGHFGcBAHb3EeWD13sUZBmFFF+WR8qHFhGdLqWBgw8AKMgyQR+mjoPXfZDFet+h2+bAf3/cDwBot6R/ui0uwceqVaswY8YMzJo1C2vWrMGkSZNCLm82m5GXl+f1R6QXPO1SlG1GQZYRZrft9Os/yT+2OaPLRHHpkBJ5HsbePhJ88HoPHpQBpHxoEcYYDrXJwSJPHcYKWaz3Pd5dVYN2i+wCzS0HUhm704WWXrSDqx587Nu3D6eccgqeeeYZPPLIIzCbzWq/BaFBuFtjcY4JkiSJ1MvS7Q0AgBPG9BPLDhbBR3eCtzI5HBT1Hp7go59b+agn5UMzdNucsDnli0aRO20SK2Sx3rdwuRgWfr9X/NtiT/3g48p/r8ThCxbH7EekevBx7bXX4rrrrsO8efPUXjWhUawOJzrcET3PZSvv8jONehw5rFj8WygfTV1wuVgCtzQ51PHgo8Bzt8zTLqR8aAeu7pkMOmQae9ceLVxOSfnQJK3dNjz7zS60dUeWPvl2e4NXmtnqcMZr01SBMYaf9jTD5nBh28GOmNahus/Hp59+ilWrVuHFF1/0e66mpkbttyM0QEuX/APU6yTkuWe5KO/yZ40oQYbiZF1RkAmjXoLV4cKBdouYBpquHORttoqArF8uL8qli49WaHVfaIqyTL32pxHzXUj50CSPfLENr63Yj9YeG+bPHRN2+X8u2wPA43NkTXHlo7HThh67HCC1dMf2HVU9+GAs/e9Uiejgd2+FWSZhmNRPEXycMKbMa3mDXoeqoizsbujCnoautA8+eJttf8VnIpQPsljXDM3uk3BBVu8nNYuCU7JY1xyMMSzZKqeTN9WGt43Y29iFZTsboZOAq48ZKgcfKa58VLd4UuKxjgGg2S5E3OFfzpIcTx6c3+VLEjBndD+/1wx1p172uNttn1q8Aws+2ZKWwe1BhccHp8z9+bRbHLDYU/tERMi0dvOi6t7VeyjXQcPltMeexi7Utspq5tYIUhI/7W0GAEwfVCQs+VO95qO62RN8xFp0SsEHEXc81uqek/LIfrkAgBmDilCa61+UPLjY0/GybEcjHv1yO55fuhv7m9OvCPVgAOUj12xAhlH+eVLRqTbgQTZ3KO0NJTztQsqH5uC+RQDQ2GkNG0Cuq24FAEweWACz+zef6spHTUuP+P9Yv6Oqp10IwpemLv/g48hhxXjx19MxIchkzyGlcvCxq6ETy3c1icf3NnVjkDswSQc6LHZ0WOViXGUdjCRJ6JeXgX1N3TjUYcFAt/cJkbq0uGs+CrNVSLu4fyut3XbYnS4Y9XSfqBW+29Hg9e9thzpwVE7wrs/1bjfTSZUFyDDItW92J4PTxcL6wSQLL+UjxpoP+kYTEeFwunDFyz/j0S+2Rf1apcEYR5IknDi2n9fdvpIh7gBj6fYGbD7gyZvuTzPXU6565GUY/AaRcYt1Uj60AU+7qKF8FGSZwK87sZ7cicRjc7jEzVKl2+slVDeIxe7EFvf5bVJVvlA+gNRWP6jmg0gYWw92YPHWerz8w96oXyvmuoSI/n3hygfvtOVFfPua0ivtciBAvQeH133E2kdPJBb+PS9QIfjQ6yQRxFDHi3ZYs78FXTYnirNN+NXkcgChg4/NB9rhcDGU5JhQUZAJs8HT9ZfKdR/VzZ60C+9mjBYKPoiI4HdfsRQ/Ngao+QhHv9wMUfNQnp+B64+VZ2HsS7Oaj0D1HhyhfGhkuu/O+g5RaNcXEa22KqRdALJY1yJL3SmX2SNKMLq/7NS97VDw4IPXe0yqLIAkSdDrJBj1suSVqsqH08VQp/idN1PahYgn/K7O7mSwO6OLyJUTbSNFp5Mw1j1+/NaTRmFEP7kKfH/aKh/+wUc/t/KhhXbbli4bTn1qGc59bnmyNyVpqKl8AB6LdTIa0w682HT2iFKM6i8X1W8/2BHULFEEH1UF4jFe95GqyseBth44FPvT0mWLqQuRCk6JiFC2U/XYnQEL4OrbLfhmWwNOn1zuZRrWHKDgNBIeO3cydtR34oQxZdjrDjr2NXeBMdZrE6dk8tiX27G/qQsPnj3RM9dF48rH+to2WOwu1Lb2oMvq8Ktf6QuIVluVgo8iUj5SluYuG/Y1dSEv04jcDAMcToZD7RZsqJWLR2ePKEFhtglGvYQumxO1rT2oKvIvGl/Hi00VwYfZqEOHNXWVD55yKc/PQF2bBQ4XQ4fVIQwkI6XvnSGImGhW2AT32JwBv2iPfrEdb66sBiTg3OlV4vFGd6tZNDUfgDzjhc95qSjIhE6S7wbqO6xCFdAaDqcLT3+9Ay4mKxtc+SgPUPPRT0M1H1sVRcH1HVYM6YPBR7OKBacAUEIW6ymJ1eHESY8vFec1X0b3zxX1WsNKc7D1YAe2HezwCz5au23Y47ZUn1Tp6fozp7jywYtNh5XloLXHjm6bEy1dtqiDD0q7EBGhVD66bYEj8oPuiySvYwDkiy2f61LYC+dHk0GHcrfTqZaLTpu6bKKI9oXvdmPN/hYA2lc+tiiCjwYNbK/aWOxOcbEoUK3mgyzWU5Hq5h40dlohSXKXmiQBRr2E4mwThpZm48Y5I8Syo92pl0B1H7zFdnBxlleqTnh9pKi5IG+zrSrK8hRFx9Dx0vduT4iYUBYV9QQJPjossjrS3mNXPOYQ/5+X2buT8qDiLNS09GBfUxcOG1LUq3UlC+WFmTGIEdqBaj7K3PNd2nrssNidXqmsVEPp5NgXh+HxgmyDTkKuSqqPcDklo7GUgt/5j+qXi89uPlrUOwRKBY/qnwegLqDTaaB6D0BR8+FIUeWDBx+FWSjKNqG2tScml1NSPoiI8K75cARcptNtltVu8QQf/P+zTPpeGyUNLJJTMFp2OeUX5iEl2V6TfQMpH3mZBpgN8meWymqC1eHEzvpO8e9U3tZ4oSw2VaseqUTUfPS9z3NnfQde+m53StY91LjPP5WFchpFkqSgx3xUf7lQfttB/xkv62paAQATKwu8Hk955cPtblpVlIlCd4Aci9cHBR9ERCi/XD22wBE5VznaezzBCf///F6qHoCsfADaTrtww7AhJdn42zkTAQD98zKQGyBfKkmSGDCXynUfu+q7vKrftZAmUhu122wBRdqlDyof9/1vM/7y8RYxoC2VUF58wzHK3W67u6ELNoWSwRjD2mo57TK5ytvlWVPKhzuVHosRHqVdiIhQfrm6bUGUD4u/8tHmTsFEW4wUiEHugi0te33wC3NZrhnHjCzF29ccGTIw65ebgermHizZVo/GThuKsk0pl3La6nNX19eVD7Uozu6b3S6MMWysky/MsbpnxhPlxTcc5fkZyM0woMPiwO7GTuH9sb6mDY2dVpgNOowr9w4+Uln5sNid4hxWVZSlUD6iNxqj4IMIC2PMy8WuJ8CPwuVi6HQHJco6Dx6I5GX2/qvG55to2WKdX5j5ML0Zg0MHErzj5Zklu8Rjj583CWdOqYzTFkYPLzblJ9m+GHx4rNXVUz54INNpdaT0nI/eYne6YNB5UhcNHVahJAW70UkmvOYjUOusL5IkYVS/XKzc14Kf9zSL4OONn6sBAHPH9/er5Upl5YMPlMs26VGYZRQBMtV8EHGhy+aETWEsFqjgtMvmAPeZ8ar5UFP5cM97aem2e72HluA1H2UBJvkG4qIjBmJSVQEmVORjlHsS8H3/25xSxmO8mG7W8BIAfTPtwu/8ovWyCUWmUWm1nXp3wWqwtroVo/7wKZ7+eqd4TFmcGayzLplwn4uBEQQfAHDy+P4AgJeW7YHD6UK3zYFF6+oAAOfOqPJbPpWVD2XgJUmSR/mIIe1CwQcRFt+oNpDy4aV29PgXnKpR85FjNohIW6tOp/VC+YjMp+SoYSX48PqZWHTjLHz8u1mYUJGPth477n5/Q0yugvGAKx9HjywF0DfTLjwtqWbahRcbA4F/c73B4XThm231Ii2aLJZsrYeLAR+6L8YAsP1Q6gYfbT128ZnxwXHhuPDwgSjMMmJfUzc+Wn8AH68/gE6rA4OKs3DEkGK/5bnyYU1F5cOn2JYb6lHBKREXfL9YgU4IvNMFkNtH+YWRF5z2ts2WM1DjRae84JQXkkaDQa/DI/MmwaiX8NWWery/plbtzYuahg4rGjtt0EnAzGGy8tHUZYUjSgt+raO2uykgjxjg842CtbfHymebDuKyhT/jwU+3qrreaNnrTqHurO9EmzvVolQ+elIs7cLrPYqzTRG7+GaZDLhi1hAAwDNLdoqUy7nTq6ALkEpLbeXDW/UppLQLEU98JbVAJ8IORRrE6WIiQPEUnKpTXuQpOtVe3QdjDA3utsnSKN1eOaP65+Km42UTo/sXbVb9ohQtXPUYXJKNikLZhZax1CwUjIbnvt2Fp7/eIS6I4eAOwAUq1nwAntSL2mkXnrvfWR986Fki2Nvo+R2vdbeeKpWPrhRTPmrcaYfKCFMunEuOHIxcswE76juxal8LdBJwzrTAdVu8BiQVaz48BmOy6lNEaRcinkSbdgE86RZPwalayofb60ODykd7j0O025VGWPMRiGuOGYbcDAPaeuyobU3u58A7Xcb0z4NeJ4n2UC3XfdS19uDBT7fikS+2Y9ZDX+PvX20PW2MklA8Vaz4AT/ChdtqFd6Yl+zjtVfyO1+xvgdPFvIKPZAfXvvB6j6oIUy6c/Ewjfn3UIPHv40aVBR0RwdNtqah8cBdrborIHU7beuxRq52aDT5SJd/dF4gk7eIXfPRwzw/1Ck4BhfKhweCDF5vmZxp75VZq0OvERa41wjvzeLHlgHyhGDNALoblhbRarvtQfrc6LA78/asdmPXg13j66x1e6UUl8Wi1BYAMkzv4UPkizPejvt0a87mUMYatB9tjNgJr6bJ51Zys2d+K6uZur5kmXamWdomi08WXy2cOEcFkoEJTjlA+UnC2C08b85o1rvQxhqjrhzQZfPz7h72Y8cBiLN5yKNmb0ifwNZAJJAH7npQ9yoe6NR/caGx3Y2fQMdWpitLjo7fwAt5kFwzytAtvISwV82hSpxsnWri0PnN4MZ6+cAqGl+Wg3eKQlZC/fY3fv7kWL323G6v2NYsLNw8C1Wy1BeKnfPCbhR67M2hAFY6vt9bj5L9/hwWfxFY3ssdd78HLHtZWt/p5xqRawWk0Hh++FOeY8ezFU3HPKWNw4ph+QZcTykeKubsyxsRNBT+HGfU6kVKP1mhMk8HHZxsPorHTiuv+sxo/7m5K9uakPbyNkH/hAvXed/jI0lzxEDUfKvh8AMDoAXnIMRtwqN2KLzZrK/j09fjoDakQfLhcDLsb5AvIKPcALV7LomXlo0ZRVHfqxHJ8fvPReOL8yRhako3WbjveX1OLv3y8BWc/uxz//akaNodLXMDjlXZRu+aj0+r53sSaeuHD0rYFmFsSCbzeY+rAQpgNOrT12PHZxoMAPAZrKZd2icLdNBDHjirDb48eGrDQlGNOUeWjrccuLBeU57CiGI3GNBl88Lsqq8OFK/+9EpvcbnjpxBs/7cdL3+1O9mYA8NR8VLjznD0BfhSdwWo+VE675JgNuOyowQCAJxfv0FT6LVqPj1Dw4COZaZdDHRbY3AZRPAfMu3iSXUvQG3jwwdsJ9ToJv5pcgS9+fzT+fflhuOXEkZg2qBAA8NH6OlHvoZPU+55zMk1xqvlQqB1cSo+WZrfzaizW2oAn+BjRLwcT3SPlP3EHH5Pdw9ZSKe3CGBOqWKQeH7GQqsoH/037po2LYpzvosngg99VDS3JRofVgQtf/BF//mgz1la3aupiFIy2bjvmv78Bf/l4S0oMleKVzHykfaD2t/ZgNR8q+nxwrpg1BNkmPTYfaNeU+uFps43M4yMUqaB88Iv0gIIMGNxDA9ND+eBeBt53twa9DseMLMXvjh+Bx86dBAD4aU+zGHRYkGUKeUcbC/wkH2yeUqwobxZiTZHx80Kss2d4seng4mxMHSgHc7wgmwcfqaR8NHRaYbG7oJM858J4kKo1H+L85XPz1GeCD4vdKS50/778MIyvyENbjx3/XLYHZzzzPc5+9gc4NVYL4Mua6hbhFtqQAsEHVz4qefARSc1Hjx1Wh1P8gNSq+QDk3vJLNah+pFvNR6D8Nw+s0kn5CMSg4mwMK82Gw8Xw4VrZIEvtNlsgjjUfaigf7vNCS5ctpt8g9/gYXJKNKQMLvJ6b4g5GumKsR4kHvNNlQH5mryd0hyJ1lQ+3cuvjUcQ7XtK+5qPRfTE26XWoLMzEe9fOxAuXTMPpk8ph0ElYvb8Vuxs6w6wltVm9v1X8fyoMleJfKp52CdztIl8Es9wycbvFLtQPSQJyIzTkiZQrZw9FtkmPTXXt+GpLvarrjhfpVvPhuUh77gJLNd7t4nC6RDthuHbK491Fg/9zu3MWqtzpAsSx5kMF5YPflDhczE/5DAdjDHvcaZfBxdki2ABkT6ChpXJLvdpBV2+obg6siKlNyiof4ubJW7ntM8pHveIELkkSTAYdThrXH09eMEVEzxs1XgOyZn+L+P/GJCsfLhdDi7uuoDxf/tFZQjicVrjVkfYeh0i55JgNqsvRRdkm/Nqtftz57nos35X6hcf8JK9G8MHvslNO+VB0u2hFkVJyoM0Cp4vBZNChJIwR3JzRZQA8xyAuwUecW22B2FUqpbFUtBee5i6b6LgZVJyFfnkZKHfXDY3qn4tsk3yzYncyr1H0ycRjsBW/eg8ghZWPIGmXWF1ONRd88DuqkgAncD6aeENNu99zWsHlYlirUD6S7RTZYXGINBbPc3aHMBnjy8jKh7rFpr5cc8wwTKjIR3OXDRf/80f8+4e9KX3BC3bnEAsppXwU+SsfFrsr5hbOZCL2qSAzbMA8bVChl3Ov2m22gMdqW00FQOlADPS+4BSI/jzFUy7l+RniTp+rHyP75YqgC0idug/h8RFDm200pK7yEfjmScx3Sfe0i2+fsZIJFXLwoWXlY2dDp1c+NtlpF/6FyjUbRLtswNku7uCDp2baLXYhxapZbKokP9OIt685EmdMLofTxfDH/23CWyur4/JevcVid4oALZa5Lr7kiW6X5H0/Ap2Ms0wG5LhTbFpMvfB9qohAWjfqdThmVJn4t9pttkB8aj58g8JY0i4Wu9PL+jzq4KPRXWxaki0eu+rooThiaBEuPWowTAYdDO7gr9ueGkGscDeNsc02UjzKR6oFH/Lv2deZtc8pH4Gk6/Hu4GNzXbvmDKg4q/e1eP27qSu5J/Bm9/sXZpuQ5ZZCbQ6XX1EvDzS80i4qe3wEIsOox+PnTcYlR8jWxd/taIzbe/UG/r01G3Sq1L8UZHJb4+ScmB1OFw60yRct38JMj9GY9oKPSIpNlRw/2hN8qO1uCihqPlS8+/cPPqI/Tr4t3s1RnqeUxaacSVUFeOOqIzGyn+wZw+vHuqzJVz5cLoZd7lrCeKdduPKRavbqwW78i7LlG6H0Vz5CDOYaVpqNDKMOnVaH+HJrjTXulAuXcBuTrXy4jWMKs03iRAj434lx06IKRdqlLc5pF44kSZg+WJZsk10jEwxlpbgk9b7+Jd/9/WjvsScl1SRqI/Q6v5ORlotOg7XZBuOYkaXCoZOfhNWEpx8sKub/uUppct9hd1gcUac2fG+KojWY4sWmQ4qzgy7Db3ZSIe3y095m1HdYkWM2CIU9XqSs8tHOz2E+ygfvdkl3kzGPt7x/8GHQ6zBmgGzzvKFWm6mX1e5i0zmj5Ur6ZPt8cCmtKMsoxnsD3icEu9Ml8pOi5qPHrvpQuVDwYDTZwVowPMVava/3ADypLJvis08kXCGoKPSvjUgP5SOy4KMw24TZI0oBAMPLclTfHo/Ph5rKh/y77J+XIS500aZefC80sSoffFxCILLM8r4HclRONO+trgEA/HLCgF7NZYoEvn6b019hThadVodIs/nebBRnm8UykU6BBjQYfAjlI0jHwHh30emmOu0Vnbb12LGjXpb2Thwry7nJLjjlUlphtgmSJHly0IqTobJtr7xAvri2WxxC+YhXzYeSVL/bVtPjAwCyTXro3Rf91p7Ef0dCKQRaHi5XG2XaBQCeOH8y3rnmSEwbVKT69sSj5oPXHuVmGGJ2pO2N8sEYEzUfQ0pCKR88+Eiu8tFjc+KTDbLz6tnTKuP+fjwgBJAynT5c9cg26ZHtkzbOyzRgZD858P7HNzsjXqfmgo/GMCdxLoltqNGe8rGuuhWAbN3L857JLjj1KB+ytJYVwO6Zn8wyjXpRdOd0MRxy1wTEO+0CQLRFtrnNzVINNT0+ADnVVJDEjpfqEBdprQ6XsztdONAW/cj0giwTpg9WP/AAlMGHehchXvORYzagn1uJi7bjxbe4MBrlo6nLhk6rA5IUun6Cp12SHXx8sfkgOq0OVBVlYvqgwvAv6CXK4ENtf5dYETdPAdyZJUnC/LljAAALv98rWpLDoangQzlVL9hJfFyFnHbZWNeW0m2XgeApl6kDC1Dsvph2WB1J/QJy5YVXNGea/KXQDreMm5thQKZRL6rU+QUqngWnnPxMo3jfZAdsgVBzrgtHtNsmYb5LjRgt7n+R1qrF+sE2C1wMEXl8JApR86Fm2iWg8hFdoNjc7UndANEptHymS3l+ZsgUhig4TXLa5b3VtQCAM6dUqu5XFAiD3tPpkyp1H/VhrrvHjirFrOElsDld+PuX2yNap6aCj/Yeh5iqF+zkMLJfLkx6HTosDjFzQStwZ9Opbv8Ao17+AiYz9cLdTbmiEUgG5spHToYBkiSJGg9+gUqE8qHTSeI7kYpFp2p6fHBEu20SlI+a5vDKh9aCj2pFKikRF5lIyIhjq22O2SC+j9GmXbjSwetcoul02OlOLQ8LUyOTFSeDtWiob7fgux0NAICzplQk7H0z4uRsGyui2DRI8CFJEu755RhIEvB5hPO2NBV88Og8L8MQNGI26nUYPUBOWWys1U7dh93pwqq9zQDkEdOSJMVsW9tbXluxD5ct/Ak7DnV4lA/ftEuAmo9cd5DBjZcOuaXcRBScAkBJrryNqXjRq2uVL9ZqeHxwkulyKpSPAOkJ/l1JpgFaLETbZpsI4lnzkZNh8KTIok67yMdWBB9RqI28ZXVYafB6DyC6tEu8ApQP1tbCxWRDucEh6lPUJtU6XhoiuHkaMyAP502vinidmgo+Is2bc78PLXW8rNnfii6bE8XZJox1d+zwKuJE38n/Y8lOfLOtAac//T22H5JPFDwQ4kGf8oQg0i7uQiTfYCMRBaeAsuMltYIPi92J3Q2y1Dyqf65q6+Wfa3sCLvIba9twy1trUdvaA5vDhQPtgT0+AE9Q5OsFkepE2+mSCOKSdhHKh9HLDj8aeMEpVy+6bM6I79K58hGuOygrQIo3EGurWzH+vs/xhw82RPT+0bBkq6x6nDG5XPV1hyLllA9R8xH62nvLSSORaYosrNBW8BGm04Xj6XjRTvDBpb2Zw0uE5FucI1/wE1nD0GNzos5dKNpjd4oTFfcwCFRwqswhA/5plkTUfACeVFyqKR87DnXC4WIozDKKHLka5Gcm7iL/p0Wb8d7qWtz7wUYcaOsBY0CGUYeSHH9jLW621WOP/IKUCkTr8ZEI4uJw6lXzIX8fo/3NcOVjUFGWqE+IdKrpTqF8hAs+IlM+Vu5thtPF8NqK/fhkw4GItiFSuEozobJA1fWGI9WUj0hr1spyM/DGVUdEtE5tBR8R5s0nKJQPrRSdLnU7c84eUSIeK3arDYl0OeX99/mZRtw4ZzgAeYIwP0kFGnTF3U1zhPLh04qVgJoPwBOUpprXx+YDchA8tjxPFYMxTqLmu+xv6sZP7pTg4q31ogCvsjAr4P7kmg3CeCsRqoxahKpjSRY8+HC4GOxOdS5E3jUf8m/mUHu0BaeeWjBejB7JTZLF7hQKk1rKhzL4vvv9DaI+obd0Wh3ijj9US3A8MKea8hGFT9Gw0sjUXU0GH+GUj5H9c2DUS2jttqPWnWsH5KmEN72xRkSzqUJrtw0baloBQBgWARAdL4lUPngl+pCSbNx60ih8eP1M/Oe3h4sAItPodh1UKh9W35oPX+UjQTUfXPlIsbTLZrfnDE+nqUWigo933QZLPM54Zoncyx+sHVWnkzyqjJaCjxRUPjIUErZa6kdHgOCjpdsesacEY0y02hbnmMRNUiTKx+6GLjAmf3eLw8zCidTnQ/m+rd123P7OelVuOve4U6UlOaaEpY45yVI+DrZZhDmkkkjTLtGgqeAjXLsPx2zQC5+MjYq6j398swsfrq3Do19si99GxsAPu5rgYsCIshz0z/dEliLtEqeC0/1N3bj2tVXi4ggAu93Bx1B3pD+pqgAzFB4GPJ/nVfPh/rLmZPjXfOh1ErJN8XUE5KRqlwU3vONTl9UiERd4l4vhvTVy8HHnyaNhNujgcLsuhlIICoTlcmqpUMFot9hFujGU5XeiMel1QkVSq+6jU/F7LcwyibRJpEF7u8UhvgOFWaaoCuP5jd/wspywKmCkaReufFx0+ECYDTp8u70Br/24P+y2hGN3o7ytQ0vUd64NB3eTTqTycajdgmMfWYLLF/7s9bjF7hQ3OGpaBWgq+BDKRwQ9+LzuQ9nxwoe2Ld3eGFfnuNZuW1RFj7zeQ6l6AEBJNlc+4nMxfXrJDny68aCXK90ehfIRCH5CsASo+cgTNR+etEueu/02EaRiq63LxbDlgFv5KNee8vHz3mZUN/cgx2zApUcOxmUzB4vnQk331JrywQPwioJMkUZIBbxchVW6EAml0myATid5ik4jTFfwgDLbpEeGUR9V2kUUm4ap9wAiT7tw5WPG4CLcefJoAMCDn2wRSpYvTZ3WCAMl941YmK6ceGA2uIfLJVD52HawAxa7Cyv3tYjuPMBz3TUZdKoqQNoMPiKIvsZXene8tFvs2F7fAUD+8f20pzku2+hyMZz+9PeY+8R3QhEIBWMMS7e76z1Glng9F0/lw+ViWLJNDnqU6hBPuwRrK8s0BjAZ86v58HxBE5VyAVJT+djf3I0umxNmg06oSWrB1YV41lXwlMspE/oj06THtccME4XFA0O4U/LBiMkwQIsF/hsYp3KAqAaZAYq8e0OnotUWAErzovP6aPIxHowm7SKKTcvC/xYiT7vI37GCLCMuO2owpg8qRJfNifnvbfBLv1jsTpzy5Hc47allYZ2Q+Y1YMoKPZCgfyvPm9zs908GVoyHUvJFM6eDDt8CKy4KR5J3Gu08iG91Fp2v3t0L5PVy8NTIjlGhp7rZhf3M3Gjqs+GFXU9jl9zZ1o7a1Bya9DocP8bZoLorijiJaNta1iS/b3qZukecLp3x4Ck49x6YjRM1HoopNAY8i1mFJriusEp5yGd0/Fwa9uj+3eCsfXjMtpsozLQqyTPjHRVNx+cwhYvhhIHhglOi5M04Xwy1vrcVfP9kS1es2xyk1pgZqD5dT1nwAULTbBg4+GGO47e11uO9/mwAoRi64z0/c1yWSm6RdEbbZAoq0izX0frd1e7yIdDoJD50zEWaDDt/taMTbq2q8lt1+qAOH2q2obe3BuurQ3ZC7G5KXduHKR0KDj87AwUdDHNyZgRQPPpR3dHanS0hlkaRdxgzIg14noanLhoPtFqxyp1x4a+DiLfVx6YRRRo/fbm8IuzxPuUwbVCh+bBxlGkHtbV28pd7r3xtr29DWbRcnkOBpF34XFkD5yPDvdklkoVZepgEm9wU+VVIvyk4XtVEGH/H4Ln+15ZCYaaGs+5k9ohT3njZWjGQPtW0tCVY+NtS24b3VtXhh6W4v6Zgxhg01bUFP5jxIHF+RgsqHimkXxpin2yXDO/hoCJJ2aey04Z1VNXj5h72oaekW52EefHCFNlx9j9PFRE1ZuDZbQDHKwR4u7eJRPgBgaGkObjlxJADgzx9t9vIw2XqgQ/z/8hA3h4wxz41YEpWPRKZdlNeuZTubxDklHu7MQIoHH22KtAW/mOh1koi0Q5Fh1GOEO7reUNMm5qb8dvZQmPQ67G/ujkvXi/IALt3eEPai8KM7/TNrRInfc/xHbXW4VB+utGSbHHzwquqNtW3Y426zLcs1+00u5AQyGetUzHYBfJSPBHl8AHJ+nAeXqdJuG69OF8BzgXe6PBcUNeEn35nDSqK2G0+W0djPinTqUkXw/97qWpz29DI88rl/sbnF7hTpgFRWPtS4C+62OYUCnGuWjxFPmwSzSFemWFfsbva02brPw0KhDRN81LbIBnUmgy6iduZsc3jFx2J3iqCsQHFduGLWEIwdkIcOiwOfrPd4f2w56KkBXL7bc3fvy8F2C7ptThh0Usj0YrwQNR9JSrs0dlqFweQO93/V7HQBUjz4UCof/IMpyTFFfCLkTqfra9qwxj03ZfaIUhwxrBiA/92/Giily5qWHhHpB4PXWIwO4HyZZTKIux41Uy/17Rasd0/9veCwgQCADbXtXm22wQhkry5GdAeq+Uhg2gUASlKs7oPfUcdD+cgw6oT6EI/UC//95WdFfww9FuuJDQJ/3qsIPnZ4go+3V1UDAL4PcLe79WAHnC6GkhwT+ql8glWDTBF89P4umAepep0k7q7DdasobzSW72oSCgev+eBBSLgizp0NsuowtCQb+gjO4Vnutv6uEGkXHtzqdZJXobtBr8NJ4+S04DrFhHOl8rF6f2vQgI47Eg8syoJR5XRpJCRT+eDHZtnORjR2WvGOO3V13OgyVd8vbp/qyy+/jPHjx6OyshIzZszAsmXLol4HN68CYhtJzus+Plhbi06rA9kmPUb1z8Xx7g9x8Vb1gw/fi97SMKkXPn442GhpfmJoVNFo7Bt3oemkynzxhdpY2+Zpsw0hM/pKwIyxALNdklNwCiTfYt1id2LRujo0dFjR0GFFfYcVkgSM7q9+8CFJUlxdTnkdUCwBZDKUD8YYVrrTqwCwbEcjHE4XGjqsosB8Z32HX6cbd0IeW56fsM6saMhQccCasjic72thFMHHit1NQuHg56aiCNMukQ6U42SZPecalyuwgsyLXAsyjX7HbnJVAQDZfh2Qvx9b3cqHXifB5nCJm1JfIjkXxpNk2Kvzmo+j3Sr89zsb8eJ3u9Fjd2JiZT6OHVka6uVRE5fg49VXX8X8+fPx9ttvo6amBnfccQd++ctfYvfu3VGtp73bX/mIJu80wd3xwh31pgwshF4nYY77grtqXwtao5jGGAl8O7m3Rai6j7ZuuwiwghkblcTBYp0X284Z3U+4we5p7MJ6t9HZ4BA+B74Opxa7S/T8B6r5UN6NJAJRJ5Mk5eOtldW48b9rcOLj3+Lpr3cAkH0jgqWxeks857u097hbqGMIIJNR87GroQvNXTaYDTrkZRjQbnFgXU0bvth8EPzaZXcy7Kjv8Hodb8dPxU4XAMh03wWrUfPR6VNsCoRXPpRBT21rjzhPFPkoHy3dtqBBAgDsqpcv6JG02QIelRUIvu8i+AigzvHgY09jF1q7bajvsKKl2w6dBJwwRr4GrNgduO5DFJtGuK1qkwyTMX7tOsM9vXfF7ia8unwfAOCm40eoHpjH5Yx4//3347bbbsOYMWMAAPPmzcMrr7yCp59+Go899ljE6+lqaQe65C9sS30LMm0WlBuc4rFwjMnTI9tuESeew8rMQFcXqszAxAIDdtR34of1+3HKhAHR7WAI2hpbkWmz4FfjKvD+mlqs21oLS2t7wCm8NXVtyLRZUJxjRJbdCtj9L5gDjC5st1nQ2tACdPX+h2B1OLFyUw0ybU4cPzAbRbBjWBZQ12rBqk01yHQxDM+Sgn7G2XYLMm0WuDoBdHWho0P+tyTJz8EhIZMx5DqscLgYimGP+HipQbnRiUybBa2NLQl9X86+/fXItFlgtVnw1rfbkAlgUlFB3Laln86BWpsFnU1twAB1nTmtbe3ItFlQyGxRb38R7PLn0MoSdhxWb6lBps2CwyoKUZRlxmebDuL7dfuwrlr+TXK27TqIcfmeU9+uPQeRabNgUoExKd+ZcOQ7bci0WeBo7+j19nU3y+ecEskg1lUsycequ8UVcP3W1navz6+62oJMAKWSA+jqQiFc4vm2xtagPinVNQ3ItFkwMlcX0X5kuBiy7BYwBnS3tCM7gOrd2SjvT399ht86CwCMydNhb2M31m+TRwJk2iwYVpqNOVU5WLpmH1ZvqQGOqvBbb01NIzJtFgzPDn4ujCc5Dqt8nu3ojMv7P/HVdvywqwn/umwGss0GWB1O2No6kAlgdnkWyo1OtHTKx3RaeS7mVGVHvh0RLicxlcvk9+/fj0GDBmHbtm0YOXKkePyFF17A448/ji1b/FvgrFYrrFbPhbe9vR1VVVVoA5Ca9yIEQRAEQfjSDiAfQFtbG/Lygl/BVU+71NXVAQDKy71HEFdUVKC2tjbgaxYsWID8/HzxV1VVpfZmEQRBEASRIqiedjEa5dybTucd14TKF82fPx+33HKL+DdXPu5//is8epE8nveyf/2EH/c04+F5E3HqxPJgq/Lj3z/sxYOfbsWIshz878ZZ4vEVuxvxm4UrUVWUiS9+f0zE6wvH4Q98hXaLAx/dOBPbD3XilrfW+b035/5FG/HGTzW4+pghuPmEUQHXt3DZHjz0+TacOnEAHp43qdfb969lu/Hw59tx+qRy/O2ciQCApdvrcfWrqwEAlUUZ+PL3xwZ9fUOHFUc/tAQAsPlPv8DyXU244t8r/fbxicXb8dnGg3j9yiMSalf9854m/PpfP2NwSRY+venohL0vZ+aDi9HcZcd71x2FMXFor/XlgY8347UV+/Hbo4fglhMDf4di5YgFi9HWbcdHN87EsLLIJlVyXC6G8fd9DsaAb+84VnWPAF8OtVlw7CPfQCcBK+4+HrkZRpz+1HfY4a4zuPmEETh6ZCnO+scPyM0w4Me7j4ckSfhgTS3mv7cB0wcX4tUrDo/rNsbK419uwwtL9+CSIwfi7lPG9mpdry7fi79+shVzx/fHY+dNFo9P//OX6LI58elNs/3cjfk5dM6YMizb3gib2/zxh7vmiN/2BS8sx9rqNjx5/hScOM7ffG5XfQdOfep75GUY8OM9J0S8vSc9/i2qm3vw+m8Px5SBhX7PP/TZFiz8fh9+M3MQ7jh5jN/z62tacd7zK1CQZURpjhk76jvxj4um4LjR/XDH2+uwaP0BzJtegcOGFKO2pQdHDitGplGP05/+3ut7kmg+Wl+H299ejyOGFmHhbw5Tdd1NnVbM+pt8Dr/sqEG4c+4YLN5yCDe8vgYTKvLw1jVHweVi+GBtLY4aVoz++VGmc9vbgfLw12jVg4/KStkJsa6uDsOHDxePHzhwABUV/rk1ADCbzTCb/fN5jUwPZMs/hAMOPXpMGcgvKRCPRcJpR43ANzVdOHd6ldfrhg8xoMeUgR1dDD3GDGSa9GCM4frXV6PL6sQ/L50etSOlxe7EIZcBMBlQ0q8YmYX56DFtw+Z2JxwZmX7r290toceUgf4DSoLuU35pAXpMGTjg0Ee138FoYEb0mDKQWZgn1jduRDl6TJsBIOS2AECWwYwek3whsZgy0a43oceUAVN+rtfrbjp9Cm46vdebGzXF/Rh6TBmotupU+byiwWJ3otauB0x6DCgvBiLwo+kt2UX56DFloMFlVHV/GWOod+rhMumRW1wAZEcXPOgAmPJz0dptR6tkQlmcj8VPO9vQY8rA+Io8eXsBHDZ+INYv2wMAOHHGUFQWZsGZmYV6pws1Nh2qirKwvsWBHlMGhg/pl/DvS6QYcnPRY8pAh97c621sleTfq7nA+/eaWZSHxuYeNMGAwT7v0en+zecU5mPUcAN+2tMMnQT5XOxuy8wuykfPISsamCHgNjYwC3pMGRhQlB3VPuhyctDTydBpCLzv9S75fJZdVBDw+VHDMuDMzMIBhwsHWh2AKQMjhw0AsjMxbVwl3traglfWN+GV9e7C06XVmFgp/6ZGludDyklOwakxTz7mbTqT6t/Lpk6XOIfv6gaQnY1DTvl6mOe+vuoAnDU7xpsZZ2SF0aqnXfr164fJkyfjk08+8Xr8yy+/xNy5c6NaV3u3p9W2yd1qWhTlXXRRtgkLf3MY5voUlZbkmFGUbQJjnkmL+5q68cmGg/h2e0NE1ui+8PZOk0GHvEwD+uVlwKSXp4AeaPN3D6x2Dz4KZWJTrHLrKG99VBq1FeeYUe6ephtu/oiycLbH7hTdOjkJ7moJBvf56LQ60GNzYm9jFz7ZcCAuDqC+HHQf40yjPmHOrvHqdum0OkShdqzt0gVxbAP2ZaXb32P6II8T60nj+gMAJlbmY2hpDkwGHUb0ky8mmw+0gzEmuh1S0VyM49th1hsCdbsASq8O/2PFTcYyTXocOVT2SOJW5uL1omMm8HmKd9Jw48RICTffpVVhrR4Is0GPMYouptwMgzjXHT+mH/rlmZFjNmD6oEJhwcA9kJLV6QLEt9tFeS3Z77Z6iMXKorfEpdX2jjvuwEMPPYTt27cDAD788EN8+umnuO6666JaD/cZcLmY+PKWRGCtHincAXX7Ibn1bpXCI+Cj9XVRr69eMXVXkiTodRIq3C201T4TFl0uJlqAg3l8AB73QbUcO1uDtKZNc9tnh0sV6HWS+GF02xx+Hh/JJtdsEMZbK/c144x/fI/r/rNa9PrHEx5gDijISJhUG8l8l06rA99sq/eblRQKHlSa9DpxvKNFzHdRuZ09ED/tlX+7hynmIx02pAhvXHUEXrhkuniMO81urmvH8t1N2HygHWaDDseNUtfDQE0yVLRX98x18f69hgoe+IU/y6THMe7PyfecxaV5fk7zhU/mjvbmkY+cCBZ4eW6mgp9/prhbbgFgTP888dssyTFjxfzjseG+k/DOtUfhn5fNwIfXz8TUgfLyRwwtCrC2xBBPnw/ltWR/czcYY2hwd7ZEMrpELeJyu3rBBRegvb0dp556Kjo7O1FZWYmPPvrIKw0TCfyE2tpjF3dhkVirR8rIfrn4cU+zsJHlFuwA8NnGg/jLGRNCzq/wJVD0WFWUhT2NXbKZ2DDPsvUdVtgcLuh1EgbkB5e0+7knTjZ1WWF3unrtttfqMweB83+/HIOZw4pxzrTKsOvINOlhdbjQY3OKPvtE+3kEQ5IklOaYUdvag+teWy1OttUtPQFzxmpyoE0+8YY6nmrDj2Oo4OOxL7bjX9/vwUNnT8S5MyIr5uZKSl6mIeZAShiNxXHqLiDby+9w30BMUlxoAOAI9506Z2x5HrBKVj54QHru9CqhMKYiHmM/FRxOgyiVHqMx/2PVowg+pg4sxMLLZviZb3HFdE8QR+cmoXxE9zlz1adLYfGuhJ9/QrnwTlZ8J0YP8K5d8v1uT6oqwLvXHoX6Dqs49yaDeCofTQrlo9vmRGOnDY0d7rlpCVQ+4nbFuPrqq3H11Vf3ah1c+eDReF6GIapgIBwj3RIsP3GtVrjdtVscWLazIeTkTl8CBR8Di+Q7Ai5vcbgSUl6QEbK2pDjbBKNegt3JUN9hRUVB77wcPKY83kFcWV4GzndbrYcjy6hHK+zosTvF7JIREboWJoKSXDn46FDMOwnnvqgGQvmItkCrFwiH0xA25htqWwH4q2+hEMFHLxQtT9olvp/9gbYeOFwMRr2EAWEuGFz5+GFnI7psTugked5TKsMvwBYV0y65PmkXrrC2BDhWXPnIdKsQgWy2B4cLPtx328VRKh/ZYVJOgdLIvigD0kichiVJSmrgASiVj3gEH97HeH9zl3A31XzaRS0sdhdsDpfni6vy3clwdwX/jvpOdFod2Oa23p07Xs4Vf7TuQMDXBfshBFQ+3AOUqpu95Uhhqx5mwJJO5/khHGwLLGlGA79DDiVThiNTkYfd6Lam5m6yqQCXDrNNeiHDh5s7oQZ8imp5ApWPSOzV+QWhwxL47jEQPO2S24vaFU/aJb7KB/9tVRRkhp37xPP/Xe7f8CkTBmBgceIHh0WDmlNtwykfgZyURfARwCiRM8TtilzfYUVXgCGHvGYv2uCDBzyB5rswxoSqFir4GFycJZyiU3FqcSA8yof6aZcmn9Ta/ubu9Kn5UJO2Hs+Y92i/uOHgykd1SzdW7GqCi8knsMtnDQEAfLH5kF/O7aP1dRhz72d48+f9fusT0WOOUvmQT2y+ysf+CIMPwCPjBypajRbPLITYP0sefOxv7sahdit0UvhakURy6sQBqCzMxNMXTcVh7lqWQHd0anNQ1HwkTvngufYOiyOgwtBusYscbzRFqR7lI3ZxNFFpl5qW0PORlORlGFFV5Dk+1xwzLMTSqUF8aj4iVz563CPtlXbnvuRnGUU9RyD1I9YbSK58dNv9A5p2iwNOdz4+kL06R5IkPH3hVDx41gRMrCyI6v2TBT/mVoXy4QxhXR8NDe4Ui8EdqO9rUgQfOYm7cdJA8GHzG2SkFsU5ZhS7O1741MupgwoxbWAh+udloNPq8JvN8t+f5KDj9Z+q/dYXrOYD8JwgOfxuTXkiDAa/wBzsZfBhsTuFjFeQHfsdLZ82yceXDyvNEYVhqcAZUyqw7M45OG5UWdihWWpS5z4+/ROofOSYDSI45YO7lOxVXAh4GjMSxFC53igfvBg23sqHu8gxkjHtgCf1Mmt4iZh8ncqo2+0iHws/5cOtHDQF+J140i7Bgw/AMw17b1OA4CPGG8hAU7Q5/HuVadQHHF+h5IihxRGnlVMBrnzYnC64XAxPLd6BSfd/IdLcvYErH3yW0ea6dhHYluQmzpNJA8GHXRTIxKMojLfeLd4iT7idOrAAOp2EX06UW3M/Wu9JvXRaHWI65vqaVr/211DBR2OnzUuOrI7ibk0t5UM5fto35xsNfMomH1+eyifwomw+4CwRNR887ZI45QMAhrvrbQIFH3u8go8o0i58qFxvaj6ygt9Nq0mNmAwd2ed++cwhOGJoEe75pb8pVSqSqWLng+hO82215cpHgOBDWXAaCj6Qck9DIOUjtnN4qLRLi2izTY1OOzVRBlNWhwsfrT+ATqsDG2vber1urkLxAnzeaJFjNiT0JlITwUdznNIugNzxAkBMZp3qPiCnTZId2r7cfFDUSSzb0QC7U16OMc9oek6g4CM/0yjy8sqCP1HzEUHw0V/UfPQy+OgJPn46GrLcP4y9TfI+pHLwURjCv0BNemxOEdwNKEhssdqw0uDBx27FhSCqtIvF0+0SK7wDIe41H+7fVaTKx+FDi/HGVUemVKowFGoFH4wxj89HRuDgI5BC2B1h8DGkRP789/goHw6nS6TeovX5yDbzlJN/4OzpdEnc3XqiULa3d1jswovKqYJfEb9pnjqo0P3vxHe6ABoJPuKVdgGAEf08rVdmg06ckCZV5mNEWQ4sdhf+t1aeSfP1Vlkd4SeDJe5/A/IPu6HDv+YD8NR98FSL1eHEwXY5kIiu5qN3Bact7gtwqLa0SPCVX8en6ChyIPQdnZrwY5NjNvRKLYgFoXw0hFY+oio4VaHbhQd+odqA1UD45RQmVnFKFBkm+TTdY3f2yizP6nCJmyc/kzH376TT6vArcvQUnIYORIeUyN9D35qPlm47GAMkKXqrBH6uDaR8ROLxoVUMep2oydhU1y5ujntb99Ftc4jjyf1MOIn0+AC0EHx0K9MucQg+FC2ikyoLRCuvJEkiR/jfn6rhcjEscSsdN8yR/UqWbm8Qxk3tPQ4x88A3gqzyabeta5XHRGca9aIKOxS8hqC3ykdbT2g3wEjxDT7GpnDwUaiQ/uPpcnogCfUenFBpF2X+PTblI7Vbbb0C+QhURC3CL8AuBnGOiYVORdo320dez8swQu++2PkqVT228AWnADDYrXzs9Qk+uJpSmGUS7xEp2ebgJmMtYdxNtQ5XP9YoDBJdvTyH8ZSL2aBDRUGmV0E5KR8+tPU4FGkX9T+ckQrlY8qgAq/nzppSAZNeh80H2vHGz9Vo6LAi26THFbOGoDjbhA6rAyvdzorcIS43w+BX/FQllA85+NivyFFHkv7gvhGHOqy9inxbuMFYL62/lS13Q0uyU8bdNBD8js7qcKnSLRAM3mabSIMxDg+ga1t7vE7SjDGv/HunzQFXhN8fT81H77tdumxO2OJglgR4B/LxSMumAsrzicXWi+DD4ul08W1J1ukkoSAo220ZY+i2R1fz0dJt9wo4Y3U3BRRt/QHTLoENE9MFftyV7sy9VT6aFE7hkiRhULHHLI6CDx9ae2yKNi31Ty5F2SZh2T7VxwGzMNuEk92eH3/5WB68NmtECTKMHpvhJdvk1Et9iD7pgT7BR6QeH5zSXDP0OglOF+vVjBePu2nvPkflSWhcCtd7APK2cjUrnh0vXPlIdLEpIBfxFWYZveYUAXIut8PqAI9vGYOX8Voo1FA+cjOM4r1DmaD1Bv5bqiyMLJDXIkaFBN+bADrYXBdOUYB2W6vDBX6zHa7bJdtsQL88+fynTL009qJmjys03QHSLm19RPlYq3De7m3w0djhnUVQzhWj4MOH1m67+DHE687m7lNG4/wZVThulL9z3/mHyXbUPE82x+3ux//L60B4vUdZgAPIgwyuePAhWL6jq4Oh10livb3peGlVqTpceRKakOKmPZIkiaFZLXEsOlXOdUkGPPWiDD74BaCyMFOcyCJNvYjgoxeqll4nidfHq902kvlI6YAaRmP82AcbAhmo3VY50C2STohA7bbN7humWOZyhRos11eUD2WXWq/TLl3ex0JpsEc1Hz7sa+ryzHWJU/Bx1tRKPHj2xIDW7UcOLcZgxQHiAcrsEaXQ6yTsrO9EtZdDnP/FRygfLd1o6bLhk40HAXg6aiLBU/cRe9FpsLku0aJMu4xP4WmgHL6/zXGsPUjGXBclgeo+eO59cHG2UDAiLTrlaZf8XnS7AJ5AN15GY6JlPU2LTTkZKnh98O9/URClgN8Nt3gFH+4BgwZdRPUaPPhQpvt60zAQarZLsFER6UKg61EvSn4AeDpb+I38IFI+gsPv3vIzjb0eqhYLkiThvBly4emEinyUudte8zONmO5uVXrws61eE219KS/IhE6S7eKfW7oLNocLYwfkYVIUluRqeH2o9WPVUtoFSEzHy4HWxM91URKo3Xa3+7cj1+XIQUQkRmMuF0OHCsoH4GmDjFe7rSftQspHOJrDBAGBlI9IPT44Ivho8tgKeIbKxZ52CRR0pXO3C4CAxmnRKh9fbT6Ecfd+hi83HwLg7zRLaZcQcGktHvUekfKbmYNx0/EjsOCsCV6P33LiSBh0Ej5efwCv/yg7nwY6gCaDTlyUXv5+LwDgwsMHRpWj7p/Xe5dTfvfZW+WD/ygGFmUJD5NUJhEup3XcYCzJaRdl8LGnUf7/ISXZIoiIJO3SZXMItbE3NR+Ap7g5XkZj1SLtkt7KhxpeH/zCUxTkXFocIEgXHh9hHEQ5wmis0fM97I1JJFc+HC7mV7Sc7sqHOaDyEV3w8ebKanTZnHh7pezI3ShSYO6aj2IKPsKSzEr2DKMevz9xpJ+Z1uFDi0VAwou5gh1AfnK0OlzIMunxq8mRp1wAdZSPVpUKtKYPLsKg4ixceLg27IqL4uy02Wl1iHRG/yQpHzz42NvUBYdbm+Wq4ZDSnKjSLjzHbNLrAp4Ao4EHuvGq+aiN0mBMq6iSdglT+BkoSI/UWp0jaj4au0Vre6wTbQFvxaXbJ/XSF5WPaIIPxhhW75OLVVfvbwVjzK/mozw/E2MG5GFUv9yYanJ6Q+oM5AhDPNps1WDe9Crsb+7GU1/vBICgvh0Di7KwYrdcaHr6pPKo21PV8PrgP9beqhUVBZn49vbjerWORFIYYmiWGvA6nNwMQ9BOgnhTnp+JTKMePXYn9jV3Y0hxtnCgjTbtIgzGMg297iDhgW48ul26bQ6Rw460c0yrZBo9RmOx0hzm5iOQy6lnqFxk3+uBxVmQJDkgb+i0oiw3o1cO1Ua9Dia9DjanC902Jwrch9nudIkbvnTvdgHkovGalp6o0i57GrtEyqux04qalh6/zlGdTsJHN84CYyxqD5beohnlI5hUmArccuJIXDFrCKYMLMAM9xRVX5QnxwtiGHAklI/22ApOGWOeO4U09UMIRpH7zihe3S51rclrs+XodBKGlcl3nTvrO1HX1gObwwWTXofygkxF2iUC5UMFd1NOvjAaU/+z550uuRmGXrv2pjqq1HyEsSwI1GobrfJhNuhR4Z7qvLdRDn4be2kSKYpOFW3i/PskSb1PDaYqSuWDD4GLRvlYta/F69+r97coCk49N/N6nQRDEuopUzr4UN50pbKBkCRJ+L9Tx+L962YKRz5fRvaXzcwmVORjYhSFphyufBxqs8bk1Nljdwp3xN6ajGmNeNd88LZCZf40GQxXFJ3ylMvA4iy55dXdtdIRifLBh4+p8D0pUaFFPBjR+uVoGX4B7k3NRywFp5HOdVHCU4Aba9tgc7jE9ylW9ZoXRX6+6aB4jKeQ8zONCb9jTxRc+cjLMIi0YjSzXXjwwT+fn/c2o7nLu+YjmaR08KGcvJjKwUcknDimHx4+ZyKevXhqTFJ2WW4GJEm2V47lIsoLd016XVQnknQg0B2dmuxyF3kOLY3MtyVe8JP+yz/sxXX/WQ3Ak4MXykc0aZdeuJtyhrnff3eAuTO9paaPFJsCnrvg3tR8hGt5Vbba8hucaLtdAHl8PQD8sKtR/Ob0OinmdO8Vs4YAAP65bI9QP/hQz0C+SukCP+ajB+QJk7lIHYoBYKU7+DjNPaF9ydYGUUgejzlp0ZLSwYdSSi1KcDGM2uh0EuZNr4q5MM5k0ImCoFjuIsWdQlbvJtpqEc9k2/gEH7yllbe7JovR/WVptqHDig6LA7kZBsybVgnAE0hElHZRwd2UM8wdEFW39PgNLIuFnfWdmP/eBrz5835srmsHkP7FpkDv0y6MMYVZY+BzKf+dOFxMqBWRDpVTMnNYCQBgxe5mHHLP3SnMMvlZukfKqRMHYHBxFlq67XhtxT5UN3fjsS+3AwB+M3NITOvUArxOa1x5nvjsIvX5aO22ic63K2cPBSCPXwDkAt1kpFl8SemC07wMI2q75B9BSQpEaslmQH4GGjqsONhmiXqMfbpXhodCWXDKGFM9+OLKx7AkKx/HjS7D7b8YBYNOwpHDijF2QJ44yYhuF2skygef69L770pZrhk5ZgM6rQ7sb+r2miIdiPp2C8wGfdAajoc+24ovNh/Cf3/yPJbuBmNA74OP9h6HqBcozA782WYY9cg26dFlc6Kly4b8TGPEQ+WUjC3PQ0GWEa3ddizZKisUvZH5DXodrjtuOO54Zz1e/G43lu1sRI/dicOGFOG86VUxrzfVueiIQXAyhsuOGoz/rJCtHCItOOUpl6Gl2RhXnod+eWYcao+95TkeJD/8CYHyziuVC04TRf88XnQai/LBh8r1vc+Rt9rancxrsqcadNscqHMrUUNLkqt86HUSrj9uOK4+ZhgmVhZ43d1EVXBq8XS79BZJkkQ6aleQ1MvBNgueWbITpz71HQ7762JMf+BL3PTGGqza1+xV32R3uvDDriYA8HIdnlBZ0OvtTHV4zYfVHpvFJW+xzDEbYDYEDyR4oM5TNLHUfOh1Eo50p14+XFcLoPc+TWdOqUBFQSYaO234bkcjTHod/nrmhJjVFC1QUZCJ+XPHYEB+pkL5iCz44CmX6YMKIUmS19yyVKj3AFI9+MhQ1nykRrSWTAb0wmLdY8jT95SPTJMeGe5WRbU7Xna7baSLsk0p3UUUU6utStOKeTpql8Jym8MYw7znf8DDn2/Dxtp2SJIcJH64tg5nP7scf/5oi1h2bXUrOq0OFGYZ8fWtx+KrW47Ge9cdhWmDCv3Wm270tuYjXLEpp9inOJsrLZF2u3BmDpdTL57fR+/O30a9DtceO0z8+7rjhokap76A3q3WRlpwuso9bZ3/NpTBBykfEaBUPvpiusAXbmAVS81Hm0ruplolXkZj/G4+2SmXcERnMqZezQfg+WwCKR/1HVZUN/dAJwELzpqAlfecgEU3zMI57lqVV5bvFRfCpdtlCX/WiFLodBKGl+X6TaJOV3qbdol0vgq/MPGuiFgKTgFP8CHWq0JgPm96JaYPKsQRQ4u8ApG+ABcxIyk4tTlcWFfTCgCYNki2fpg6qEA8nyolDKkdfLjvvFKlQCbZcOWjpjkG5aMrvcdPh0O026ocfPA7u2SnXMKhtFcP16rtqflQpyQslPKx+YBcNDq0NAcXHDYQxTlmTKjMxyPzJmFCRT4cLob/rZWl+6U7GgEAs0eU+K0n3eHKQ6zBR0uEwQefTcUHZXp8PqL7LgwuzhJ+H4A6wYfZoMc71x6FN646MmTqKB2JJu2yqa4NVocLhVlGEfiPK8+HUS+vg5SPCOA551RoC0oFRrqL9bYcaI+q5QrwzHVJdzOmYMRruJxQPspSW/ngaReHi4W9gKmtfAx1Bx+7Gzr9Ah/esTJmQJ7f686eWgEAeG9NLVq7bVjvvps7ekSpKtulJXo72yVS5YOPhxDBhz262S4cSZJw1LBi8e9UueBplWjSLl+4h8jNGFwkiuszjHrRpJDoGS7BSOngI999t0b1HjIj+uXAZNChw+rA/ubu8C9QoNZcF60Sr3ZbrSgfWSa9MBsKl3ppU7nmY1BxFnSS/L4NbrdLzha38jE2QPBx2qRyGHQS1te04eUf9oIxYGS/HGG415dQq+YjnALBixH5cYql24UzS6FQJXMwaDqgj1D5sDlcYojcWVMrvZ679cRROH1SOU4a2y8+GxklKR18HDW8BOMr8jBvemX4hfsARr0OY9xOqRvr2qJ6rafbpY8rHyqmXVwuht2NXPlI7eBDkiSF14d/0em2gx3CMZQ/n69CtwsgXzir3C6Vu+q9Uy88+BgzwL8FtzjHjONGlwEAnlkiz06a3QdVDwCiYDrWtEukBaeluXJg5592iT74OGqYIvgg9bpXRBp8LN5yCI2dNpTmmnH8mDKv52aNKMGTF0xJGRUqpYOP8oJMfHTjbMxL417uaOHS2Yba6IKPdB8/HQ6P8qFet0tdWw8sdheMekkTXhO5QVxOD7VbcPrTy3DqU8twqN2CDqt6Ph8cXvexWzFqvcfmFDbwgZQPwJN6sTvlk25frPcAIGocept2CdeR5Zt28RScRh+IluaacdLYfhiQn4FR/UP7uxCh4cFHOJ+P13+S/UDOnV4JY4rXSaa0yRjhDw8+NtW2R/W6Pt/tks2Hy6mnfPCUy6DibE0URPMaKl+vj+92NMLqcMHqcOGud9eDn9/UHNg1tCQbX8Nb+dh2qAMuJkv9wfLQx40uE4ZVJoMOhw8pDrhcusOLBR1R1npxWiJMu/DjwAeQeRxOYyvwfO7iaZAk9DlXZbXRSeGVj+rmbnznLso+b3r0w0sTTeqfMQkvJiiUj0gHzHlNtO2jygdXfNTsduHFpkNLUrvYlBNsvsv3OxvF/y9xz8ww6XVeI717C09LKdttPSmXvKAXJ7NBj9MmlgMAZgwujEn+Twd4cOtwxhZ8RJ52kYOPTqsD3Tb5D4gt7QLIXRoUePQefQT26m/+LNd6zB5RkvQhl5FAyofGGNEvB0a9hLYeO2paekQuPRSdVoe4Y+q7yod80m1VMfjgykeq13twPEZjHuWDMSaCj8lVBVhb3QpAVj3UvGgESrsog49Q/O74EbDYnfj1kYNV2x6twQeL2SMd7uEDdzgNV7yfbdIj06hHj92Jxg6bqDHpa8MoUw3e7RIs7WJ3uvCWu9D0gsNSX/UASPnQHGaDXrTcboyw7oOrHhlGnaia72tEUvNhd7rw3Y4GcbcXDs0qH4qC0531najvsMJs0OGfl04XFv5qWKsr4X4DNS09om7B02Ybuh6gNNeMh+dNwoTK6OYZpRM8fx9L2qXb5oDFbcsebkyFJElC/ahr6xG1NhR8JJdwPh9bD3SgvsOK/EwjThiTGt0s4aDgQ4Pw1EukHS917mmGqdLfnQyKfIbLBeKtldW45J8/4cnFOyNap9aUj0Aup1z1mDG4CMU5Zvz5jPGQJGBkmboFgkXZJuRnGsEYsKexCy4Xw9aDHQCAsQP6blARKQZ97MpHk7t+w6TXITuCIIKfJ/Y3edr5+2q6K1UQDqdBzl2tPfIxHpCfAZOK6dJ4QmkXDTKuIh/4uRobIiw63eGeujo8ySPfkwlPNzldDO09joBma9vcF8MdhzrCrq/T6sBB94C/YSnu8cEJVPOxbKc8qI3bYZ84th8W33IM+uWp66UhSRKGlWZj9f5W7GroRLZJnnRr0uvE4DkiOEZd7DUfvNOtKNsUUSqNu5zua5aDa71OgkkDBdXpTLiC0073DUWuSq7EiYC+URpkguh4iazodCcPPjRyhx4PMox68cNs6Aw8G4crRL6zc574agfmPPoNGhUGWfuaPAPltOIam+vj8+FwuvDjbh58eLpIhpbmINus/kmM13Y8+OlWfLrxAABew0SnoXAYRLdLDMpHhMWmnJJcebn97jEOWUY9FY0mmXA+H7w9PicOv9t4Qb96DTK6fy70OglNXbaIhszx2oS+HHwAELMmaluDBR/y44favZ9/d3UNdjd0Ybl7nDsg1y4A0IS/B8c37bK+tg0dVgfyM40YVx7/1Mf1xw3HoOIs1LT0YMGnWwEE9/cgvPGkXVjEXW6cZnfaJVKX0dIcWfXa7w6wKeWSfMIVnHLlI0dFb554Q8GHBskw6jHCHUhEUnRKyocMH8zHFQ5f6trkx5u6bLA65KJIl4vhgPtxpaU9Dz4qC1O/pY0jHE7daZcf3PUeRw4tFndW8aS8IBNvX3MkRisMp8J1uhAyPO0CRDZcTElzlEMlec3HPvf3nYpNk0+4gtNOUj6IRMHNxh79Yjve+rk6aIdGp9Uh1JHhpX3bZbDcrXwcCBB8dNscoisIAOrb5RRLY6dVVPxXK4IP/v+VGlI+cn26XZa5g4+ZCXQNLcvNwJtXHYnDBhfBqJdw9Mi+6VgaLVz5AKLveIk27cKDD/57iHaiLaE+nsFygZ/vcN9QUM0HEXd+OXEADDoJ2w514I531+OIvy7GpgDdL7vcqkdprlkztQnxojxE2qXO5zFeTFqrCFSqWwIpH9oJPnj7bIfFgUPtFqzc2wIAmDU8sQFAfpYRb159BNbcexKGq9xVk64o62Ki7XiJ1N2U49sVR8pH8hH26mGUj1xSPoh4c9yoMvwwfw7uOHkUynLNaLc4sHR7o99y1Onigdd8BEq78NQK56BbLVIGJd5pF7fyEYHJW6qg7HZ5bcU+OFwMMwYXYkgSfEokSdKURJxsDIq0WLQdL0L5iLTmg4KPlCNc2qVD1Hxo5zdFwYeGKcvNwHXHDsc50+Spvwfb/C+qVO/hgdd8+AYaAHDAV/kQwYdn2bpWCxxOFxhjqNViwak7+LDYXXh1xT4AwOUzhyRzk4gIUdbk2KPseGkW7qYRdrv4BCmxznUh1CNswSnVfBDJQBRSBuh8oeDDA0+71LVZ/OTLWh81JFDaxeliONBmQXuPQ7S2VRRoR/lQ3hW1dttRUZCJE8dqww2xryNJkme4XJTKR7QFp2aDHvmKoYKkfCQfXm8cTvmgmg8ioQzIly+qBwMEH9Rm66F/fgYkCbA5XEKK5nA1hBflBQo+ALnQlNd+lOSYNNWGqNdJXjnhXx85SBPTeAkZQ4xGY/y7HmmrLeCdeqGC0+TjKTgNZzKmnbo+OvOkAf1FOsE7+LA6nMIMawQFHzDqdSjjcyt8ggpe2zGlqgCAf9qF33Xub+4WxaYVGmqz5fA7o0yjHufP0MYAKkJGeH1EkXaxO13irrgozFA5JdzlFCDlIxWItOCU0i5EQuFpl8ZOK2wOz4lpb2M3XEy+4PTluS5KRLutT90H9/iYOqgQgH/wMdkdlFS3dItiUy3Ve3C40djZ0yr6fPeT1hDD5aJQPnjKRSfBK5USjpJcCj5SCVFwGkT54K22VHBKJJSibJOYvaB051TWe5A9skygdlvGmCg4nTKwAABQ32FBl9WBFrfXwRFDZfvx/c09mjQY45w2qRzDSrNx9dHDkr0pRJTwjpdoWm0bOtzFpjnmqIzklMqHllKL6YooOA1w6Bljmmy11c6WEkGRJAn98zOwv7kbB9stqHK3f+6olwekUZuth/IALqet3Xb0uMe8T6osgCTJNtYb3O6xuWYDxpXLTpzVzd3ocRu6acnjg3P9ccNx/XHDk70ZRAwI5SMKk7EG9zyikpzolE+lUppF3S5JJ9Rsl26bE/xhUj6IhBOo7oM6XfwJlHbhKZeSHBOyzQZxol69v0W8hqsc1YqaDy0GH4R2EcPlolA+Gt3KR7RpV6/ggwpOk44uRMEpVz30OklTbdEUfKQJvO5D6fVBwYc/gdIuvNiUdw31d4+TX72v1f2aDAwsloOPpi4b9jTKRbxaTLsQ2sWTdole+SjthfJBaZfkE6rgVBiMmQ2aSq/HJfjYtGkTTjnlFFRWVmLgwIH49a9/jcZGf/dNQj18lQ+ni2G3+yJJwYeHQC6nXAUpL5A/Q/5ZrlEoH3kZRlGwZ3UX9ZLyQSQST9ol+pqPktzI22wB6nZJNXhHfCjlQ0udLkAcgo+mpibMmTMHc+fORXV1NbZv3w6Hw4ELLrhA7bciFAzI48qHHHzsaeyEzeFClkmPKrpDF3CFqKHDKibXci8PX+WD+yNwtWSgwkq9NNeMDA1JnIT2McRgMtbYKX+HSfnQNiLtEuDYa3GoHBCH4GP16tU47rjjcOONN0KSJGRkZGD+/Pn46quv0NYWfvw7ERv983ktgxx8bKprBwCM7p8r2rQIuTPIbHB3BrXJd4W804WrIlz54PDHq4o8SgepHkSi4SZj0XW7yN/taGs+irJN4KcNqvlIPvzYB1Q+NOhuCsQh+DjxxBPxxhtveD22YcMGmM1mmM2BfwBWqxXt7e1ef0R0eGo+5JPNlgNyp8tYd5cGISNJkggmuOLB0y4DeNolzzv4KBfBh0f5oHoPItEIe/Voul1iLDjV6yQMKpYHDpaRR1DSCWWv3kFpl8B8/vnnuPbaazF//nxkZGQEXGbBggXIz88Xf1VVVfHerLSDBx/1HfLws80H5ABu7ID8ZG5WSsKDDF734Vdwmu8bfMj/HugVfJDyQSQWYa8eRfARa9oFAJ6/ZBr+fflhIvgmkocoOA2hfORoyFodiDL4aGhoQGVlZdC/hx9+WCzrdDpx991346yzzsKf//xn/PGPfwy63vnz56OtrU38VVdXx75HfZTiHDMMOgkuJle4b3anXUj58Kc839Nu63QxMcclUNpFJwH93EqIsnaG6miIRBNtq63V4URbj1wPEIvD8ch+uThmZGnUryPUR8x2CRB4arXgNKqtLS0tRU1NTdjlLBYLzjzzTDQ1NWH16tUYNWpUyOVDpWSIyNDrJPTLy0Btaw/W17ShsdMKnQSM6peb7E1LOZTttvUdFjhdDAadJE7QyrRLv7wM0WVAygeRTKK1V+eqh1EvRWWtTqQeOqF8yI6mypZaKjhVcPHFFyMnJwfLli0LG3gQ6sHv2JdsrQcADCnJpkr1AHCFo6alG4u3yJ9Vv7wMIW1mmw3CplgpOZcXZIplKPggEo3w+Yiw1ZYbjJXkmDXl/0D4o1ccP1/xQ4vW6kAc7NXfeustbNq0CWvXroXJFF1vOdE7ePDxtTv4GFtO9R6B4DUf3+1oxHc7ZP+ZYT5eKP3zM9BR3+kVfJgMOtx58igcbLNiSEl24jaYIBC98hFrsSmReig7Fp0u5jWnR5iMaUz5UH1rP/30U9TU1GDYMP/BVY8//jjmzZun9lsSbrjXR737pDNmAKVcAjGkJBuSBDAGFGQZce70Klw5e4jXMv3zM7CjvlMUm3KuooFsRJLgNR+RttrG6m5KpB7KYMO36LRP1HxEwsKFC7Fw4UK1V0tEgG+XxtgBVGwaiMrCLDx38TRY7E78Ylz/gGZhY8vz8N2ORkyoIPWISA2i7XZRpl0IbaNMu/gWnXZo1OdDW1tLhIS3inKo0yU4vxjXP+Tzt500CmdOqaCCXSJlMEbZ7SKUD0q7aB6dojrT12jMYzKmraJiCj7SiAGKFEFJjhlluYF9VYjwGPU6jO5PwRuROnjSLlTz0dfwKjh1pUfahabaphEDFGkXqvcgiPTCk3aJsNuFlI+0Qa8LlXaRW221VnBKwUcaUZpjFvMYKOVCEOmFMcrBcg1U85E2SJIELn4o0y6MMc222lLwkUYY9DqRaqFiU4JILwx6PliO0i59EZ56UQpf3Tan8P0g5YNIKr+aXI5BxVmYNbwk2ZtCEISKGHV8sFz4tEu3zYEumxMABR/pAvf6UCofXPXQ6yRkBujaS2W0FSoRYZl/yhjMP2VMsjeDIAiViUb5aOyQrdUzjDpkk8txWuBRPjzHXxiMmQ2ac7El5YMgCEIDRDNYrqFTHpZYmkvW6ukCLzpVFpxqtdMFoOCDIAhCExijMBlrcCsf5G6aPugCFJxqdagcQMEHQRCEJojGXp0bjFGnS/rAlQ9l2qVTo+6mAAUfBEEQmsAQxWA56nRJP/QBCk47KO1CEARBxJNoul3IYCz90EkBaj7ERFttWasDFHwQBEFogmi6XUj5SD88aRfPY1RwShAEQcQV4XAagfJB7qbph1A+qOCUIAiCSBR8tktEPh+Udkk7PK22nuBTq9bqAAUfBEEQmiAan4+mTrnVtiSbgo90wRN8eB4TJmOkfBAEQRDxwJN2Ca189Nic6LHL1upFOaa4bxeRGMhkjCAIgkg4kaZdmrtl1cOkJ2v1dELYqzN/e3Wq+SAIgiDiQqRpl5YuOfgozDaStXoaoQukfIjgg1ptCYIgiDhg1Edmr97Mg48sSrmkE+7DH3CqLaVdCIIgiLhg0EVmr97iTrsUZVPwkU4Enmort9pSwSlBEAQRF4wR2qsL5YOCj7TCN+3CGKNWW4IgCCK+GCI0GePBRzEFH2mFb8Gpxe4CF0GyKfggCIIg4kHE3S5U85GW6Hx8PmyK9BtXxbSE9raYIAiiD2KMtNuFaj7SEr2Pvbqy64XXA2kJCj4IgiA0gBgsF2m3CwUfaYVnsJx8/HkQqpM8qoiWoOCDIAhCAxh1kfp8yB0QRZR2SSt8C055yzVPx2kNbW41QRBEH4MrHy7m3W7pS1MXpV3SEXfWTaRdeNcTL0TWGhR8EARBaADlRcYepOOFMUY1H2mKb9qFfwe0WO8BUPBBEAShCYwKeT2Y10e7xSFk+YIs7VluE8HRBSk4NWiw0wWg4IMgCEITKJWPYMEHn+uSbdIjw0hD5dIJP+XDScoHQRAEEWeUF5lgaRc+0ZY6XdIP34JToXxQ8EEQBEHEC0mSxIUmmPLR3En1HumKx+dD/rfdSWkXgiAIIgHw1Euw4XLNVGyatvimXUj5IAiCIBICLzp1BGm15TUf5PGRfvgWnHK/F2q1JQiCIOKKIYzFOtV8pC88u0ImYwRBEERCERbrVPPR5/CzV3eR8kEQBEEkAGGxHqTbhRuM0UTb9MM37SIKTqnmgyAIgognYZUPslZPW4IXnGrzMq7NrSYIguiDhKv5aOl2D5Wj4CPt4MqHw9dkjNIuBEEQRDwJ1+3iUT7IWj3d4MqHr726ntIuBEEQRDwJ5fNhd7rQ1iMrH1TzkX74FZy6U29GMhkjCIIg4gmv+QjkcNrqTrlIEpCfScpHuiGUD3fc6SCTMYIgCCIRhOp24Z0u+ZlGzVpuE8Hh9uouRq22BEEQRALxpF38lQ/qdElvfAfLeVpttXkZ1+ZWEwRB9EF4fj+g8kHW6mmNXvItOHUrH5R2IQiCIOIJv9AEUj6aushaPZ3hmTSXr/JBaReCIAginoQqOCXlI73xTbt4Wm21eRnX5lYTBEH0QYz64AWnNFQuvfFNu3CjOSMpH4E588wzIUna/HAIgiBSCV5cGCjtwpWPYgo+0hL/wXLaLjg1xHPlL7zwAnbv3h3PtyAIgugz+NqrM8awdEcjPt90EIu31gMg5SNd8QyWk/8tgg+NKh9xCz62bduGP/zhD3j77bdx7LHHxuttCIIg+gy+9uovLN2NBZ9uFc8XZhkxfVBhUraNiC++yoeY7aLRbpe4BB92ux0XXngh/vCHP2DQoEFhl7darbBareLf7e3t8dgsgiAITeNrr76zvhMAcNSwYlx19FAcOawYZoM+adtHxI9gBadaDT7ikiz6wx/+gOLiYtx4440RLb9gwQLk5+eLv6qqqnhsFkEQhKYx+nS7dNucAIBfjOuPY0eVUeCRxvgWnHpabftAzUdDQwOmTJkS9PmbbroJ06dPx7/+9S+sW7cu4kLT+fPn45ZbbhH/bm9vpwCEIAjCB+Hz4e526bI5AABZJgo60h1fnw9uMqbVqbZRBR+lpaWoqakJ+nxLSwsmTpyIf/zjHygvL494vWazGWazOZpNIQiC6HP4+nx0W2XlI9sc194BIgXQ+bXa8qm22gw+VNVr1q1bh5qaGpx77rmQJAmSJGHIkCEAAEmScPHFF6v5dgRBEH0Ko0+3CykffQe9T82HQ+MmY6qGy8ceeywY8+4/37t3L4YMGeL3OEEQBBEdwufD5V3zQcpH+iO6XXym2pLyQRAEQcQVX5+PLispH30FkXahqbaRMXjwYFI9CIIgVMCTdvFRPkykfKQ7Hp8P+d/UaksQBEEkBGXahTHmqfkwk/KR7vgWnAqTMUq7EARBEPFEWXBqsbvARWVSPtIf34JTz1RbCj4IgiCIOMJbbe1Oj+oBAJlGUj7SHeHz4ddqq83LuDa3miAIog/C8/sOl0t4fGSZ9MJ6m0hfeNqFBx0OjZuMUfBBEAShEZT26h6PD0q59AX8W23JZIwgCIJIAMrBct3u4CObik37BHqfVlsHtdoSBEEQiYBfaBwuhi6RdiHloy8gptr6mIxRqy1BEAQRV5TdLkL5IIOxPoFB+Hz4KB9UcEoQBEHEE69uF658kLV6n8Bf+aBWW4IgCCIBGJXdLqR89Cl4zQd3OOUW+1RwShAEQcQVg1e3C9V89CWCT7Wl4IMgCIKII6LbxeVCt5W6XfoSvvbqnlZbbV7GtbnVBEEQfRCjjpSPvorer+CUul0IgiCIBODx+WBU89HH4AKHr/JBPh8EQRBEXBGtti4Xdbv0MXTBTMao4JQgCIKIJ3pF2oWUj76FX9qFTMYIgiCIRMAvNHYnKR99DWXBqcvF4I5ByGSMIAiCiC9isJyLlI++hkf58NR7KB/XGhR8EARBaASe33e6GDqtNNW2L6FXOJzylAtAJmMEQRBEnDEqOhvaenjwQcpHX0BZcErKB0EQBJEwlJ0N7T12AGQy1ldQBhl2h0L5oFZbgiAIIp4ogw+b22SK0i59Az7bBQCs7uBDJ3kGzmkNCj4IgiA0QqC73GwKPvoEykPPgw+tGowBFHwQBEFoBp1Ogu+NbibVfPQJlGkXGw8+NFpsClDwQRAEoSmUvg4mvQ4mA53G+wI6r7SL7PGi1WJTgIIPgiAITWFUXHCyqNi0zxBI+dDqRFuAgg+CIAhNoVQ+qN6j7xCo4JSUD4IgCCIhKE2lyOOj76DsauFpFyMFHwRBEEQiUHY40FyXvgVXOqx2XnCq3Uu4drecIAiiD6LscKC5Ln0LnnrhHi9anWgLUPBBEAShKZRFhmQw1rfgopdH+aDggyAIgkgAyrtdslbvW3Dlw9Nqq91LuHa3nCAIog9iIOWjzyJqPkSrLSkfBEEQRAIwUs1Hn8U3+KBWW4IgCCIhGLxMxkj56EvwYEOYjFHahSAIgkgE3iZjpHz0JXSSt/JBBacEQRBEQvAyGSPlo0/hq3xQ2oUgCIJICEqTMVI++hY6n24Xmu1CEARBJARve3VSPvoSVHBKEARBJAUv5YN8PvoUfgWnVPNBEARBJAIDKR99Fi50kMkYQRAEkVCUeX5SPvoW/q22pHwQBEEQCcDLXp2Ujz4FtdoSBEEQScHbXp2Uj76Ef6utdi/h2t1ygiCIPoiXvTr5fPQpaLYLQRAEkRR4t4tOAswGOoX3JXx9PqjVliAIgkgI/G4322SAJGn34kNEj3+rrXYv4drdcoIgiD4ILzLMok6XPodeIpMxgiAIIgnwtAt1uvQ9eH0ptdoGwel04o9//COGDBmCiooKTJ06FR9//HE83oogCKJPYSTlo8/ib6+uXf0gLqHz7373O2zYsAE//fQTSktLsWjRItxyyy049thjkZ2dHY+3JAiC6BPwVltyN+178IJTWxr4fKj+7d25cyeee+45bN++HaWlpQCA0047Daeccgr0eorUCYIgegM3GaOJtn0PUXDq1H6rrerBx0cffYQJEyZg2LBhXo+HCjysViusVqv4d3t7u9qbRRAEkRYUZZsAAKW55iRvCZFo9D7dTVpOu6i+5Tt37sTYsWPx7LPPYuLEiRg6dCjOPfdc7N27N+hrFixYgPz8fPFXVVWl9mYRBEGkBadMGICHzp6IW04clexNIRKMzqfAVMvKR1TBR0NDAyorK4P+Pfzww3A6nfjiiy+wZ88erFixAhs3bkR5eTmOOeYYdHZ2Blzv/Pnz0dbWJv6qq6tV2TmCIIh0I8Oox7kzqtA/PyPZm0IkGH/lQ7vBR1Rpl9LSUtTU1IRcZsGCBSgqKsJDDz0kHnv00Ufx0ksv4dtvv8Uvf/lLv9eYzWaYzSQhEgRBEEQwfIMNI6VdPMyePRt2ux2MMfEYYwySJFGAQRAEQRAx4pt20bLyoXrwMWvWLAwbNgy33norrFYr7HY77rzzTpSXl2PWrFlqvx1BEARB9AkMPsGGlltt46LZvPXWW2hubsbAgQMxaNAg7N69G1988QUyMihHSRAEQRCxoJN8C061m3aJi0tNUVERXn755XismiAIgiD6JL6xBqVdCIIgCIKIK34Fp5R2IQiCIAginvimXchkjCAIgiCIuOLfakvKB0EQBEEQccRf+aDggyAIgiCIOOIbbBg03O2i3S0nCIIgiD4EFZwSBEEQBJFQKO1CEARBEERC8c2yaNlkTLtbThAEQRB9iHSaakvBB0EQBEFoAN/BcjTVliAIgiCIuOKnfFDBKUEQBEEQ8cRf+aDggyAIgiCIOOJb40E1HwRBEARBxBXftAuZjBEEQRAEEVf80i5U80EQBEEQRDzxjTUo7UIQBEEQRFzxn2qr3Uu4drecIAiCIPoQyrSLJPmnYbQEBR8EQRAEoQGUBadaVj0ACj4IgiAIQhMolQ4t13sAFHwQBEEQhCZQKh8GDXe6ABR8EARBEIQmUKodWp5oC1DwQRAEQRCaQE9pF4IgCIIgEomX8kHBB0EQBEEQ8UanqPnQ8kRbgIIPgiAIgtAE3sqHti/f2t56giAIgugjKGtMqeaDIAiCIIi4o/NqtdX25VvbW08QBEEQfQTvVltSPgiCIAiCiDNKkzFKuxAEQRAEEXd0VHBKEARBEEQiIZMxgiAIgiASio5muxAEQRAEkUiUaoeBlA+CIAiCIOKNnlptCYIgCIJIJMoaU2q1JQiCIAgi7ngXnGr78q3trScIgiCIPoIy7UJTbQmCIAiCiDs6arUlCIIgCCKRUMEpQRAEQRAJhVptCYIgCIJIKMq0C5mMEQRBEAQRd7zSLqR8EARBEAQRb5TdtVTzQRAEQRBE3KFWW4IgCIIgEgqZjBEEQRAEkVCo4JQgCIIgiIRCBacEQRAEQSQUL58PKjj15+2338aMGTNQWVmJwYMH47e//S3q6+vj8VYEQRAE0Scgk7EQfPjhh7jiiivw6KOPoqamBhs2bEBHRwdOOeUUtd+KIAiCIPoM3vbqFHx48dlnn+GEE07A0UcfDQDIzc3F/PnzsWrVKjQ3N6v9dgRBEATRJ1AWnBqp28WbadOm4ccff8TBgwfFYx9//DHGjh2LoqKigK+xWq1ob2/3+iMIgiAIwhueetH6VFuD2iu84oor0NDQgCOOOAJz587F1q1bMWTIEHz11VdBX7NgwQLcf//9am8KQRAEQaQVekmCE6xvpV0aGhpQWVkZ9O/hhx+GxWJBTU0Nhg4diunTp2PSpElYtmwZfv7556DrnT9/Ptra2sRfdXV1r3eMIAiCININnm0xaDztEpXyUVpaipqampDLXHXVVWhoaMDixYshuYtjLr74YsycORObNm3C8OHD/V5jNpthNpuj2RSCIAiC6HPwotM+pXxEwrJly3DMMceIwAMApk+fjuzsbKxevVrttyMIgiCIPgMvOqVWWx+OO+44PP/889ixYwcAwGaz4b777oPdbsfMmTPVfjuCIAiC6DPwQlOtm4ypXnD62GOPYcGCBTj11FPR1dUFp9OJI444AkuXLkVFRYXab0cQBEEQfQaedtH6VFvVgw+z2Yz77rsP9913n9qrJgiCIIg+jS5NWm21rdsQBEEQRB/CU3Cq7cu3treeIAiCIPoQ+ZlGr/9qFdXTLgRBEARBxIeH503EzvpODC/LSfam9AoKPgiCIAhCI0ysLMDEyoJkb0avobQLQRAEQRAJhYIPgiAIgiASCgUfBEEQBEEkFAo+CIIgCIJIKBR8EARBEASRUCj4IAiCIAgioVDwQRAEQRBEQqHggyAIgiCIhELBB0EQBEEQCYWCD4IgCIIgEgoFHwRBEARBJBQKPgiCIAiCSCgUfBAEQRAEkVBScqotYwwA0N7enuQtIQiCIAgiUvh1m1/Hg5GSwUdTUxMAoKqqKslbQhAEQRBEtHR0dCA/Pz/o8ykZfBQVFQEA9u/fH3LjOTNmzMDPP/8c8fqjWT5ey7a3t6OqqgrV1dXIy8tL2nbEa93R7l+8tiPaZaNZPp7HMNrl6Xsa27L0PU3cdsRzWfqeJmY7IlmWMYaOjg6Ul5eHXE9KBh86nVyKkp+fH9EHrdfrIz4g0S4fr2U5eXl5qu9jqnweQOT7F8/tiOfnAcTnGEa7PH1Pe7du+p4mZjvoe9q7dWvlexqJaJAWBafXX3993JaP17LREs/tSPd9jOfnEc/1psrnEQ2pcly0uI/0Pe3ddkRDqhwXLe6jWtsssXBVIUmgvb0d+fn5aGtrizry1Qrpvo/pvn8A7WM6kO77B9A+pgPpuH8pqXyYzWb88Y9/hNlsTvamxI1038d03z+A9jEdSPf9A2gf04F03L+UVD4IgiAIgkhfUlL5IAiCIAgifaHggyAIgiCIhELBB0EQBEEQCYWCD4IgCIIgEkrcgg+Xy4UVK1bglltuQVFREV5++WWv59euXYs5c+agvLwcFRUVuOWWW2CxWLyWWbx4MY455hhUVlZi0KBBOPfcc7Fr1y6vZVasWIHZs2dj4MCBGDFiBF544YV47ZIfidrHvLw8lJeXo7KyUvzdcccd8d49Vfbv7bffxsSJEzFgwACMHDkSzz33nN/7aP0YRrKPyTqGAPCvf/0L48ePR0VFBUaPHo1nn33W63mr1Yq77roLw4cPR3l5OU4//XTU1tZ6LVNbW4vzzjsPgwcPRkVFBX7/+9/DarV6LZPM45iofUzWcVRj/xoaGvDvf/8bRx99NIYMGRLwfbR+DCPZR63/FmtqanDeeeehqqoKlZWVOOOMM7B3716vZZJ5HCOGxYmXXnqJzZgxg91zzz2spKSELVy4UDx36NAhVlxczJ555hnmcrlYa2srO/3009lll10mllm1ahUzm83srbfeYowxZrFY2M0338wqKytZd3c3Y4yxLVu2sNzcXPbOO+8wxhjbtGkT69evH3vzzTfjtVsJ38fW1lYmSRKzWCwJ2Sclvd2/L7/8kuXl5bEffviBMcbY1q1b2ciRI9nLL78sltH6MYxkH5N5DF955RVWWVnJNm7cyBiTP+8BAwaw1157TSxz+eWXs6OPPpq1tLQwu93Ofv/737MJEyYwh8PBGGPMarWyMWPGsFtuuYXZ7XbW0tLCZs+eza699lqxjmQex0TtY7KOoxr7xxhjkyZNYueffz676KKL2KBBg/zeR+vHkLHw+6j136LNZmOjRo1id9xxB7PZbMzhcLDbbruNjRkzhtntdrHeZJ5TIyVuwYeSQYMGeZ3UX3zxRTZ69GivZZqampjRaGQHDx5kjDH24IMPsilTpngt09raygCwVatWMcYYu+KKK9ipp57qtcwjjzzi97pEEK993LhxIysrK4vvxkdALPt30UUXsWuuucZrmffff5+NHz9e/FvrxzCSfUzmMbzuuuvY66+/7vXYLbfcws4880zGGGP79u1jOp2OrVy5UjxvtVpZcXEx+/DDDxljjL366qusqKiIWa1WsczKlSuZyWRiDQ0NjLHkHsdE7WOyjqMa+6dk4cKFAS/MWj+GSoLto9Z/i+vXr2fHHnssc7lcYpn29nYGgK1bt44xllrn1FAkpeajra1NzG/hmM1mMMawfPlyAMC0adOwfft2bN26VSzz8ccfo6ysDCNHjgQAfP311zjttNO81nPaaadhzZo1OHToUJz3IjRq7WNNTQ0qKysTt+EREsn+BVomMzMTGzduRGtrKwDtH8NI9jGZx/CZZ57BBRdc4PXYhg0bhEviN998g379+mHatGnieZPJhJNOOgmffvopAPkY/eIXv4DJZBLLTJs2DcXFxVi8eLFYJlnHMVH7mKzjqMb+RYLWj2EkaP23OGHCBCxZsgSSJHmtAwByc3MBpPY5VUlSgo8zzjgDu3fvxt///nfY7XY0Nzfjt7/9LbKysnDw4EEAwAknnIAnnngCp5xyCi6//HKceuqpeOedd/Ddd98hJycHAFBXV+c3Oa+iogIA/PJkiUatfaypqYHZbMb111+P0aNHY+zYsZg/fz66u7uTuXsR7d8FF1yAV199FV9//TUYY9i2bRseeOABABDLaP0YRrKPqXIM7XY7brzxRixfvhy33XYbgMCfPyAfA/75x7pMMo5jPPcxFY5jrPsXCVo/hpGQCscQUG8fV61ahXnz5uGyyy4TNS6pchzDkZTgY9iwYfj222/x2WefYdiwYTjxxBNx1llnYdCgQTAY5EG7TqcT+/fvR//+/TFjxgxMnToV69evx7fffivWYzQa/e46lRFhMlFrH61WKzo6OnDxxRdj06ZN+OKLL7B8+XJcccUVydo1AJHt34UXXojnnnsOd955JwYNGoQbb7wRf/rTnwBALKP1YxjJPqbCMdy3bx9mz56NxYsXY9myZRg/fjyAwJ8/4H0MYl0m0ccx3vuY7OPYm/2LBK0fw0hI9jEE1NvHJ598ErNnz8Zll12Gl156STyeCscxIhKR2/HNpQfCbrezzMxM9vXXXzPGGHvggQfY9OnTmc1mE8vs2bOH5ebmsm+++YYxxtjo0aPZiy++6LWenTt3MgAiJ58o4rWPgVixYgXT6XSss7NTlW2PhFj2LxDLli1jRqNRFHxp/RgGwncfA5HIY7hy5UpWWlrKbr31Vr9teuONN1hFRYXfay6++GJRy3LNNdewiy66yG+ZyspK9sYbbzDGkn8cE7GPgUjUcezt/ikJVg+h9WOoJNg+BkJLv0XGGHM6nezyyy9nI0aMYCtWrPBbPtnHMVKS5vPhK3N9/vnnMJvNOPLIIwEAy5Ytw8yZM2E0GsUygwcPxvDhw/Hjjz8CAE4++WR88sknXuv58ssvMXnyZPTr1y/OexAeNfYRkNtBlTidTgDJj2bD7V+gZT744AMcf/zxYkCS1o9hoGV89xFI3jHct28fTjnlFDzzzDN45JFH/AZTzZkzB/X19Vi/fr3Xti1ZsgRz584FIB+jL774Ag6HQyyzdetW1NfX4/jjjxfLJOs4JmofgeQcRzX2LxK0fgwjRcu/RQC4/fbbsX37dqxcuRKHH3643/uk+jlVkIgIx/eOcsOGDaysrIz99NNPjDE5KhsxYgR75plnxDIPPfQQ69+/v1jG4XCwF154gRmNRlENvGPHDpaXlycqgbdt28YqKirYf//730Tslhfx2scHH3yQnXjiiay2tpYxxlhdXR2bOXMmu+SSSxK0ZzKx7N8LL7zApk6dKqLtzz77jBUUFIhOHsa0fwwj2cdkHsO5c+ey++67L+QyV111FTv++ONZW1sbczgc7M4772Tjxo0TrXt2u52NGzeO3XXXXczhcLDW1lZ2/PHHs6uvvlqsI5nHMVH7mKzjqMb+KQmmCmj9GCoJto9a/y2uWLGClZSUsMbGxqDrSKVzaiiSlnZZuHAhGzNmDCsvL2ejRo1iL7zwgtfzTqeT/f3vf2cTJkxg5eXlrF+/fuyEE05gixcv9lpu6dKlbPr06ay8vJwNHz6cPf/88/HenYDEax97enrYPffcw4YNG8YGDBjAysvL2e9+9zvhA5IoYtk/q9XK7rzzTjZw4EBWXl7OjjjiCPbdd9/5rVvLxzCSfUzmMQTAysrKWEVFhd8fh/vLVFRUsP79+7PTTz+dVVdXe62nurqanX766WzAgAGsoqKC3XzzzX6ycbKOY6L2MVnHUa3944RKSWj9GHKC7aPWf4v33Xcfy8jICLiORx99VCyXKufUUEiMMZZU6YUgCIIgiD4FzXYhCIIgCCKhUPBBEARBEERCoeCDIAiCIIiEQsEHQRAEQRAJhYIPgiAIgiASCgUfBEEQBEEkFAo+CIIgCIJIKBR8EARBEASRUCj4IAiCIAgioVDwQRAEQRBEQqHggyAIgiCIhPL/iTc91zupvygAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# データの読み込み\n",
    "df = py4macro.data('jpn-q')\n",
    "\n",
    "# トレンドからの％乖離のデータの作成\n",
    "df['gdp_cycle'] = 100 * (\n",
    "    np.log( df['gdp'] ) - py4macro.trend( np.log(df['gdp']) )\n",
    ")\n",
    "\n",
    "# プロット\n",
    "# ax = df.plot(y='gdp_cycle')\n",
    "ax = df['gdp_cycle'].plot()\n",
    "ax.set_title('GDPのトレンドからの乖離（％）', size=20)\n",
    "ax.axhline(0, c='red')\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "このようなGDPの変動を説明する方法として２つある。\n",
    "1. 決定的（deterministic）な過程で生成された時系列として捉える。\n",
    "1. ランダム（stochastic）な過程で生成された時系列として捉える。\n",
    "\n",
    "１の考えによると，差分方程式$x_{t+1}=f(x_t)$のように来期のGDPは今期のGDPに依存している。マクロ変数の持続性を捉えるには必要不可欠な特徴と言えるだろう。しかし，今期のGDP（$x_t$）が与えられると来期のGDP（$x_{t+1}$）は自ずと決定さることになり，来期のGDPの予測は簡単なものとなる。もしそうであれば政策運営は非常に簡単であろうが，現実はそうではない。そういう意味では，１は現実を十分に捉えることができていない。\n",
    "\n",
    "一方，２の考えはランダム変数の実現値の連続としてGDPが観測され，今期のGDPが与えられても来期のGDPにはランダムな要素があるため，予測が難しいという特徴がある。この特徴こそが，マクロ変数の性質を捉えるには必要な要素であり，上のプロットに現れていると考えられる。主流のマクロ経済学では，消費者や企業の行動はフォーワード・ルッキングであり（将来を見据えた最適化行動であり），且つ経済全体ではランダムな（不確実な）要素が重要な役割を果たしているという考え基づいている。そのような分析枠組みの中で，景気循環のメカニズムを解明することが目的となっている。\n",
    "\n",
    "以下では，まず，ランダム変数について復習し、マクロ変数を捉えるにはどのようなランダム変数生成過程が妥当かを検討する。\n",
    "また、シミュレーションを通して、その統計的特徴を視覚的に確認する。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "## ランダム変数の統計的特徴：復習"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "### ２つのランダム変数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "#### 説明"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`2`つのランダム変数$X_i$と$Y_i$, $i=1,2,3,\\cdots,n$を考えよう。\n",
    "例えば，$X_i$と$Y_i$は$n$個の`2`セットのサイコロ（合計`2`$n$個）を同時に投げた場合の目と考えることができる。\n",
    "また、$X_i$の単位は円であり、$Y_i$はドル表示だとしよう（例えば，$X_i$のサイコロの目が`5`であれば`5`万円，$Y_i$のサイコロの目が`3`であれば`300`ドル）。\n",
    "`2`変数の**不偏分散**は次のように定義される。\n",
    "\n",
    "$$\n",
    "\\sigma_{X}^2=\\frac{1}{n-1}\\sum_{i=1}^{n}\n",
    "\\left(X_i-\\overline{X}\\right)^2\n",
    "\\qquad\n",
    "\\sigma_{Y}^2=\\frac{1}{n-1}\\sum_{i=1}^{n}\n",
    "\\left(Y_i-\\overline{Y}\\right)^2\n",
    "$$\n",
    "\n",
    "ここで$\\overline{X}$と$\\overline{Y}$は平均を表している。\n",
    "（不偏）分散は、各ランダム変数の「散らばりの度合い」を数値化したものであり、$X_i$のの単位は$\\text{円}^2$、$Y_i$の単位は$\\text{ドル}^2$となる。\n",
    "**標準偏差**は不偏分散の平方根である\n",
    "\n",
    "$$\n",
    "\\sigma_{X},\n",
    "\\quad\n",
    "\\sigma_{Y}\n",
    "$$\n",
    "\n",
    "となり、$\\sigma_{X}$の単位は円となり、$\\sigma_{Y}$の単位はドルである。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "次に、`2`変数の相関を考えたい訳だが、その尺度として共分散が使われ、次のように定義される。\n",
    "\n",
    "$$\n",
    "\\sigma_{XY}=\\frac{1}{n-1}\\sum_{i=1}^{n}\n",
    "\\left(X_i-\\overline{X}\\right)\\left(Y_i-\\overline{Y}\\right)\n",
    "$$\n",
    "\n",
    "符号の解釈：\n",
    "* $\\sigma_{XY}=0$：無相関\n",
    "* $\\sigma_{XY}>0$：正の相関\n",
    "* $\\sigma_{XY}<0$：負の相関\n",
    "\n",
    "共分散の絶対値が大きければ大きい（小さい）程，相関度が高い（低い）ことを意味するが、その値は単位に依存することになる。\n",
    "$\\sigma_{XY}$の単位は円xドルである。\n",
    "\n",
    "また上の定義から次が成立することが簡単に理解できる。\n",
    "\n",
    "$$\n",
    "\\sigma_{XX}=\\sigma_{X}^2,\n",
    "\\qquad\n",
    "\\sigma_{YY}=\\sigma_{Y}^2,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "共分散の特徴は$X_i$と$Y_i$の単位に依存することである。\n",
    "例えば、`2`つのランダム変数$K_i$と$Z_i$の単位がユーロと人民元としよう。\n",
    "$\\sigma_{XY}$と$\\sigma_{KZ}$を計算できるが、単位が異なるため比較には向いていない。\n",
    "その点を克服するのが**相関係数**であり、次のように定義される。\n",
    "\n",
    "$$\n",
    "\\rho_{XY}=\n",
    "\\frac{\\sigma_{XY}}{\\sigma_X\\sigma_Y}\n",
    "$$\n",
    "\n",
    "次の特徴がある。\n",
    "* 分母は必ず正となるので，分子の共分散が符号を決定する。\n",
    "* $\\rho_{XY}$の値は`-1`から`1`の間の値を取り、単位に依存しない。この特徴は、分母に$X$と$Y$の標準偏差の積を積を置く事により分母の単位をキャンセルしているためである。\n",
    "\n",
    "更に、$\\rho_{XX}$を考えてみよう。\n",
    "\n",
    "$$\n",
    "\\rho_{XX}=\n",
    "\\frac{\\sigma_{XX}}{\\sigma_X\\sigma_X}\n",
    "=\\frac{\\sigma_{X}^2}{\\sigma_X^2}\n",
    "=1\n",
    "$$\n",
    "\n",
    "同じ変数は完全に相関するため相関係数は`1`となる。\n",
    "一般的には，$\\rho_{XY}$の絶対値は`1`よりも小さな値となる。\n",
    "相関係数の重要な特徴は単位には依存しないため，単位が異なる変数の相関度を比較するには有用な指標となる。\n",
    "即ち、$\\sigma_{XY}$と$\\sigma_{KZ}$を比較して、どちらが相関度が高いかを容易に確認できることになる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "#### `.cov`と`.corr()`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "共分散と相関係数の違いを説明したが，`DataFrame`を使ってどのように計算するかを説明する。`dfex1`は次のような`DataFrame`になっている。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "def create_example(n):\n",
    "    rng = np.random.default_rng()\n",
    "    df = pd.DataFrame({'X':rng.normal(10, 1, size=n),\n",
    "                       'Y':rng.uniform(0, 100, size=n)})\n",
    "    return df\n",
    "\n",
    "dfex1 = create_example(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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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       "\n",
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       "\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>Y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>10.875352</td>\n",
       "      <td>5.333614</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10.065056</td>\n",
       "      <td>41.035620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>11.744110</td>\n",
       "      <td>77.021350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>11.819713</td>\n",
       "      <td>74.705772</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>11.437074</td>\n",
       "      <td>82.617324</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>8.487176</td>\n",
       "      <td>87.610043</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>11.889709</td>\n",
       "      <td>77.796288</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>9.806767</td>\n",
       "      <td>61.264819</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>9.647793</td>\n",
       "      <td>88.071896</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>11.290295</td>\n",
       "      <td>51.462952</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           X          Y\n",
       "0  10.875352   5.333614\n",
       "1  10.065056  41.035620\n",
       "2  11.744110  77.021350\n",
       "3  11.819713  74.705772\n",
       "4  11.437074  82.617324\n",
       "5   8.487176  87.610043\n",
       "6  11.889709  77.796288\n",
       "7   9.806767  61.264819\n",
       "8   9.647793  88.071896\n",
       "9  11.290295  51.462952"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfex1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "`DataFrame`には分散と共分散を計算するメソッド`.cov()`が用意されている。\n",
    "結果を`vcov`に割り当てよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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>X</th>\n",
       "      <th>Y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>X</th>\n",
       "      <td>1.320684</td>\n",
       "      <td>-2.506850</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Y</th>\n",
       "      <td>-2.506850</td>\n",
       "      <td>676.331109</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          X           Y\n",
       "X  1.320684   -2.506850\n",
       "Y -2.506850  676.331109"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vcov1 = dfex1.cov()\n",
    "vcov1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`vcov`は分散共分散行列と呼ばれる。\n",
    "左上と右下の対角線上にあるのは、`X`と`Y`の不偏分散（$\\sigma_{X}^2$と$\\sigma_{Y}^2$）である。\n",
    "一方、右上と左下の値（同じ値となる）が共分散（$\\sigma_{XY}$）である。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "相関係数はメソッド`.corr()`を使って求めることができる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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>X</th>\n",
       "      <th>Y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>X</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.083878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Y</th>\n",
       "      <td>-0.083878</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          X         Y\n",
       "X  1.000000 -0.083878\n",
       "Y -0.083878  1.000000"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfex1.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "右上と左下の値（同じ値となる）が相関係数（$\\rho_{XY}$）である。\n",
    "一方、左上の値は`X`と`X`の相関係数（$\\rho_{XX}=1$）であり，右下の対角線上にあるのは、`Y`と`Y`の相関係数（$\\rho_{XX}=1$）である。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`vcov1`を使い相関係数を計算することもできる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.08387822546247928"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vcov1.loc['X','Y'] / ( vcov1.loc['X','X']**0.5 * vcov1.loc['Y','Y']**0.5 )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 時系列のランダム変数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "#### 説明"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "マクロ経済学では，時系列データを頻繁に扱うことになる。難しく思う必要はなく，基本的には上で説明した概念を「時系列的」に再解釈するだけで良い。既出のランダム変数$X_i$と$Y_i$，$i=1,2,3,\\cdots,n$を時系列データとして次のように置き換えてみよう。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* $X_i\\;\\Rightarrow\\;\\varepsilon_t,\\quad t=0,1,2,3,\\cdots$\n",
    "* $Y_i\\;\\Rightarrow\\;\\varepsilon_{t-1},\\quad t=1,2,3,\\cdots$\n",
    "\n",
    "$X_i$の例として，**同時**に投げた$n$個のサイコロの目と考えることができると説明したが，同じ例を使うとすれば，次のようになるだろう。\n",
    "* $\\varepsilon_0$は第`0`期に投げたサイコロの目\n",
    "* $\\varepsilon_1$は第`1`期に投げたサイコロの目\n",
    "* $\\varepsilon_2$は第`2`期に投げたサイコロの目\n",
    "* $\\cdots\\cdots$\n",
    "\n",
    "同様に$Y_i$を考えることができる。違いは，$\\varepsilon_{t-1}$は`1`期前の値を表していることだけである。\n",
    "従って，\n",
    "* 第`1`期では\n",
    "    * $\\varepsilon_t$は第`1`期に投げたサイコロの目\n",
    "    * $\\varepsilon_{t-1}$は第`0`期に投げたサイコロの目\n",
    "* 第`2`期では\n",
    "    * $\\varepsilon_t$は第`2`期に投げたサイコロの目\n",
    "    * $\\varepsilon_{t-1}$は第`1`期に投げたサイコロの目\n",
    "* 第`3`期では\n",
    "    * $\\varepsilon_t$は第`3`期に投げたサイコロの目\n",
    "    * $\\varepsilon_{t-1}$は第`2`期に投げたサイコロの目\n",
    "* $\\cdots\\cdots$\n",
    "\n",
    "ここで第`0`期の$\\varepsilon_{t-1}$の値は存在しないことに注意しよう。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "更に，$\\varepsilon_{t-1}$を次のように一般化しよう。\n",
    "* $\\varepsilon_{t-s},\\quad t=s,\\;s+1,\\;s+2,\\;s+3,\\;\\cdots,\\quad s\\geq 1$\n",
    "\n",
    "一見すると複雑に見えるが，$s=1$と置けば$\\varepsilon_{t-1}$になることが分かる。\n",
    "$\\varepsilon_{t-s}$は単純に$s$期前の値を表しているに過ぎない。\n",
    "従って，\n",
    "* 第`s`期では\n",
    "    * $\\varepsilon_t$は第`s`期に投げたサイコロの目\n",
    "    * $\\varepsilon_{t-s}$は第`0`期に投げたサイコロの目\n",
    "* 第`s+1`期では\n",
    "    * $\\varepsilon_t$は第`s+1`期に投げたサイコロの目\n",
    "    * $\\varepsilon_{t-s}$は第`1`期に投げたサイコロの目\n",
    "* 第`s+2`期では\n",
    "    * $\\varepsilon_t$は第`s+2`期に投げたサイコロの目\n",
    "    * $\\varepsilon_{t-s}$は第`2`期に投げたサイコロの目\n",
    "* $\\cdots\\cdots$\n",
    "\n",
    "ここで第`s-1`期以前の$\\varepsilon_{t-s}$の値は存在しないことに注意しよう。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "以下では，次のように置き換えて説明するが，分かりづらければ`s=1`として読み進めれば良いだろう。\n",
    "* $X_i\\;\\Rightarrow\\;\\varepsilon_t,\\quad t=0,1,2,3,\\cdots$\n",
    "* $Y_i\\;\\Rightarrow\\;\\varepsilon_{t-s},\\quad t=s,\\;s+1,\\;s+2,\\;s+3,\\;\\cdots,\\quad s\\geq 1$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "まず$\\varepsilon_{t}$と$\\varepsilon_{t-s}$の分散を考えてみると，次のように置き換えることができる。\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\sigma_X^2&\\quad\\Rightarrow\\quad\\sigma_{\\varepsilon_t}^2\\\\\n",
    "\\sigma_Y^2&\\quad\\Rightarrow\\quad\\sigma_{\\varepsilon_{t-s}}^2\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "$X_i$と$Y_i$の分散は，`s`期ずれているだけの同じランダム変数$\\varepsilon$の分散に置き換わっている。\n",
    "* 解釈\n",
    "    * $\\sigma_{\\varepsilon_t}^2$：$\\varepsilon$の`0`期から`t`期までの値に基づく分散\n",
    "    * $\\sigma_{\\varepsilon_{t-s}}^2$：$\\varepsilon$の`0`期から`t-s`期までの値に基づく分散\n",
    "* $\\varepsilon$の単位が円であれば，分散である$\\sigma_{\\varepsilon_t}^2$と$\\sigma_{\\varepsilon_{t-s}}^2$の単位は$\\text{円}^2$となる。\n",
    "* 標準偏差は分散の平方根である$\\sigma_{\\varepsilon_t}$と$\\sigma_{\\varepsilon_{t-s}}$になり，単位はそれぞれ円となる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "更に，共分散は次のように置き換える事ができる。\n",
    "\n",
    "$$\n",
    "X_i\\text{と}Y_i\\text{の共分散}=\\sigma_{XY}\n",
    "\\quad\\Rightarrow\\quad\n",
    "\\sigma_{\\varepsilon_t\\varepsilon_{t-s}}\n",
    "=s\\text{期間離れた}\\varepsilon\\text{の自己共分散}\n",
    "$$\n",
    "\n",
    "ここで$\\sigma_{\\varepsilon_t\\varepsilon_{t-s}}$を**自己共分散**と呼んでいる。\n",
    "「過去の自分との共分散」という意味で「自己」が追加されている。\n",
    "* 解釈\n",
    "    * 自己共分散はランダム変数とその`s`期前の値との**相関の度合**を示す指標。\n",
    "    * $\\varepsilon$の単位が円であれば，自己共分散$\\sigma_{\\varepsilon_t\\varepsilon_{t-s}}$の単位は$\\text{円}^2$となる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "これらの結果を使うと$\\varepsilon_t$の相関係数は\n",
    "\n",
    "$$\n",
    "\\rho_{XY}=\n",
    "\\frac{\\sigma_{XY}}{\\sigma_X\\sigma_Y}\n",
    "\\qquad\n",
    "\\Rightarrow\n",
    "\\qquad\n",
    "\\rho_{\\varepsilon}(s)\n",
    "\\equiv\n",
    "\\rho_{\\varepsilon_t,\\varepsilon_{t-s}}\n",
    "=\\frac{\n",
    "    \\sigma_{\\varepsilon_t\\varepsilon_{t-s}}\n",
    "    }{\n",
    "    \\sigma_{\\varepsilon_t}\n",
    "    \\sigma_{\\varepsilon_{t-s}}\n",
    "    }\n",
    "$$\n",
    "\n",
    "で与えられ，一般的には**自己相関関数**と呼ばれる。「関数」と呼ばれる理由は，$\\rho_{\\varepsilon}(s)$は`s`の関数として考えることができるためだ。このサイトでは，`s=1`の場合は**自己相関係数**と呼ぶ事にする。\n",
    "次の特徴がある。\n",
    "* 分母は必ず正となるので，分子の自己共分散が符号を決定する。\n",
    "* $\\rho_{\\varepsilon_t\\varepsilon_{t-s}}$の値は`-1`から`1`の間の値を取り、単位に依存しない。この特徴は、分母に$\\varepsilon_{t}$と$\\varepsilon_{t-s}$の標準偏差の積を積を置く事により分母の単位をキャンセルしているためである。\n",
    "\n",
    "解釈は次のようになる。\n",
    "* $\\rho_{\\varepsilon}(s)=0,\\;s=1,2,3,\\cdots$：何期離れたとしても自己相関はなしという意味である。過去の影響は皆無の状況を指している。\n",
    "* $\\rho_{\\varepsilon}(s)>0,\\;s=1,2,3,\\cdots$：今期と`s`期前の値は正の相関があるということを示す。$\\varepsilon_{t-s}$の値が大きければ（小さければ），$\\varepsilon_{t}$も大きい（小さい）傾向にあるという意味であり，`s`期前の影響が強ければ，自己相関係数の絶対値は大きくなる。経済学では`s=1`を考える場合が多く，この性質を**持続性**（persisitence）と呼ぶ。持続性は多くのマクロ変数の重要な特徴となっている。\n",
    "* $\\rho_{\\varepsilon}(s)<0,\\;s=1,2,3,\\cdots$：今期と`s`期前の値は負の相関があるということを示す。$\\varepsilon_{t-s}$の値が大きければ（小さければ），$\\varepsilon_{t}$は小さい（大きい）傾向にあるという意味であり，`s`期前の影響が強ければ，自己相関係数の絶対値は大きくなる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### `.cov()`，`.corr()`，`.autocorr()`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "自己共分散と自己相関係数の違いを説明したが，`DataFrame`を使ってどのように計算するかを説明する。`dfex2`は次のような`DataFrame`になっている。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "def create_example(n):\n",
    "    rng = np.random.default_rng()\n",
    "    df = pd.DataFrame({'X':rng.normal(10, 1, size=n)})\n",
    "    df['X_lag'] = df['X'].shift()\n",
    "    return df\n",
    "\n",
    "dfex2 = create_example(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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>X</th>\n",
       "      <th>X_lag</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12.228754</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>7.791301</td>\n",
       "      <td>12.228754</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>10.986207</td>\n",
       "      <td>7.791301</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>9.747251</td>\n",
       "      <td>10.986207</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10.428973</td>\n",
       "      <td>9.747251</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>9.190174</td>\n",
       "      <td>10.428973</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>9.032098</td>\n",
       "      <td>9.190174</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>10.836912</td>\n",
       "      <td>9.032098</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>9.192634</td>\n",
       "      <td>10.836912</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10.324616</td>\n",
       "      <td>9.192634</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           X      X_lag\n",
       "0  12.228754        NaN\n",
       "1   7.791301  12.228754\n",
       "2  10.986207   7.791301\n",
       "3   9.747251  10.986207\n",
       "4  10.428973   9.747251\n",
       "5   9.190174  10.428973\n",
       "6   9.032098   9.190174\n",
       "7  10.836912   9.032098\n",
       "8   9.192634  10.836912\n",
       "9  10.324616   9.192634"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfex2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "行ラベルは時間と考えよう。`0`番目の行が`0`期を表し，`9`期までの値が含まれる。\n",
    "`X_lag`は`X`を`1`期ずらした値となっている。\n",
    "例えば，`1`期の`X_lag`の値は`0`期の`X`の値が入っている。\n",
    "また，`-1`期はないため，`0`期の`X_lag`の値は`NaN`になっている。\n",
    "それぞれの列は次のように$\\varepsilon$に対応している。\n",
    "* `X`$\\quad\\Rightarrow\\quad\\varepsilon_t$\n",
    "* `X_lag`$\\quad\\Rightarrow\\quad\\varepsilon_{t-1}$\n",
    "\n",
    "`dfex2`のメソッド`.cov()`を使って分散共分散行列を表示しよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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>X</th>\n",
       "      <th>X_lag</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>X</th>\n",
       "      <td>1.567853</td>\n",
       "      <td>-1.115650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X_lag</th>\n",
       "      <td>-1.115650</td>\n",
       "      <td>1.746945</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              X     X_lag\n",
       "X      1.567853 -1.115650\n",
       "X_lag -1.115650  1.746945"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vcov2 = dfex2.cov()\n",
    "vcov2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* 左上の値：`X`の分散（$\\sigma_{\\varepsilon_t}^2$）\n",
    "* 右下の値：`X_lag`の分散（$\\sigma_{\\varepsilon_{t-1}}^2$）\n",
    "* 右上と左下の値（同じ値）：`X`の自己共分散（$\\sigma_{\\varepsilon_t\\varepsilon_{t-1}}$）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "自己相関係数はメソッド`.corr()`を使って求めることができる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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>X</th>\n",
       "      <th>X_lag</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>X</th>\n",
       "      <td>1.00000</td>\n",
       "      <td>-0.82027</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X_lag</th>\n",
       "      <td>-0.82027</td>\n",
       "      <td>1.00000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             X    X_lag\n",
       "X      1.00000 -0.82027\n",
       "X_lag -0.82027  1.00000"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfex2.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "右上と左下の値（同じ値）が自己相関係数（$\\rho_{\\varepsilon_t\\varepsilon_{t-1}}$）である。\n",
    "一方、左上の値は`X`と`X`の相関係数（$\\rho_{\\varepsilon_t\\varepsilon_t}=1$）であり，右下の対角線上にあるのは、`X_lag`と`X_lag`の相関係数（$\\rho_{\\varepsilon_{t-1}\\varepsilon_{t-1}}=1$）である。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`X`の列を`Series`と抽出し，メソッド`.autocorr()`を使って自己相関係数を計算することもできる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.820269694415106"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfex2['X'].autocorr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "メソッド`.cov()`を使って自己相関係数を計算する場合は，次のように`dfex2`から欠損値がある行を削除した後に分散共分散行列を計算する必要がある。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.8202696944151061"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfex3 = dfex2.dropna()   # 欠損値がある行の削除\n",
    "vcov3 = dfex3.cov()\n",
    "\n",
    "# 自己相関係数の計算\n",
    "vcov3.loc['X','X_lag'] / ( vcov3.loc['X','X']**0.5 * vcov3.loc['X_lag','X_lag']**0.5 )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true,
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "## ホワイト・ノイズ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "### 説明"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "時系列のランダム変数$\\varepsilon_t$，$t=0,1,2,3,\\cdots$を考えよう。例えば，レストランの経営者の収入。ビジネスにはリスク（競争相手の出現やコロナ感染症問題）があるため変動すると考えるのが自然である。$\\varepsilon_t$は$t$毎にある分布から抽出されると考えることができる。次の３つの性質を満たしたランダム変数をホワイト・ノイズ（White Noise）と呼ぶ。\n",
    "1. 平均は`0`：$\\quad\\text{E}\\left[\\varepsilon_t\\right]=0$\n",
    "1. 分散は一定：$\\text{ E}\\left[\\varepsilon_t^2\\right]=\\sigma^2$（$\\sigma^2$に$t$の添字はない）\n",
    "1. 自己共分散（自己相関）は`0`：$\\text{ E}\\left[\\varepsilon_t \\varepsilon_{t-s}\\right]=0$（全ての$s\\ne 0$に対して）。\n",
    "\n",
    "＜コメント＞\n",
    "* 平均`0`と分散が$\\sigma^2$のホワイト・ノイズを次のように表記する。\n",
    "\n",
    "    $$\n",
    "    \\varepsilon_t\\sim\\textit{WN}(0,\\sigma^2)\n",
    "    $$\n",
    "    \n",
    "* ホワイト・ノイズの例：\n",
    "    * 平均`0`，分散$\\sigma^2$の正規分布から抽出された$\\varepsilon_t$\n",
    "    * 最小値`10`，最大値`100`からからランダム抽出された$\\varepsilon_t$\n",
    "* 正規分布や一様分布ではない分布でもホワイト・ノイズになる。\n",
    "* ホワイト・ノイズは独立同分布（Independentt and Identically Distributed or iid）の１つである。\n",
    "    * ホワイト・ノイズは上記の`3`つの性質が満たされれば良いので、毎期の分布が同じである必要は**ない**。\n",
    "    * ホワイト・ノイズに必要な$\\text{ E}\\left[\\varepsilon_t \\varepsilon_{t-s}\\right]=0$は**線形**の相関がないことを要求しており、非線形の相関があっても構わない。一方、`iid`の「独立」は線形・非線形のいかなる相関もないことを意味している。`iid`はより制限がより強い概念となる。\n",
    "    * 共分散は`0`だが独立ではない例\n",
    "        * $X$は標準正規分布に従うランダム変数とし、$Y=X^2$としよう。この場合、$\\text{E}\\left[XY\\right]=\\text{E}\\left[X^3\\right]=0$となる（左右対称が理由）。一方で、$X$と$Y$は明らかに非線形の相関がある。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "### 平均と分散"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "以下では実際にランダム変数を発生させ，そのプロットと統計的な特徴について考察する。まず，平均と分散について確認するために，その準備として次のコードを実行しよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "rng = np.random.default_rng()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "`rng`はランダム変数を生成する「種」となるオブジェクトとして理解すれば良いだろう。\n",
    "\n",
    "正規分布を生成する構文は次のようになる。\n",
    "\n",
    "`rng.normal(loc=0, scale=1, size=1)`\n",
    "```\n",
    "    loc：平均（デフォルトは0）\n",
    "\n",
    "    scale：標準偏差（デフォルトは1）\n",
    "\n",
    "    size：ランダム変数の数（デフォルトは1）\n",
    "```\n",
    "ここで、`.normal()`は`rng`のメソッドである。例として、平均`5`，標準偏差`2`の標準正規分布から`10`のランダム変数を生成しよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.16913764, 2.09997477, 7.50390508, 5.45960427, 1.8954103 ,\n",
       "       4.85261246, 5.13625562, 4.67149123, 7.0575845 , 5.59707286])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng.normal(5, 2, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "```{note}\n",
    "`NumPy`を使いランダム変数を生成する方法については，[「経済学のためのPython入門」のNumpy: ランダム変数](https://py4basics.github.io/8_NumPy_random.html)を参考にしてください。\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "では、標準正規分布からのランダム変数を`n`個抽出しプロットしてみよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 100\n",
    "\n",
    "vals = rng.normal(size=n)\n",
    "\n",
    "dfwn = pd.DataFrame({'WN':vals})\n",
    "\n",
    "dfwn.plot(marker='.')\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "２つの特徴がある。\n",
    "* 平均`0`：`0`を中心に周辺を動いている。\n",
    "* 分散一定：`0`から外れても`0`に戻っている。標準正規分布の場合、`-2`から`2`の間の値を取る確率が約`95`％になる性質からも理解できるだろう。\n",
    "\n",
    "平均と分散を計算してみよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.22156203227936383, 1.0441674619608863)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfwn['WN'].mean(), dfwn['WN'].var()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "標準正規分布の母集団からのサンプル統計量であるため誤差が発生していることがわかる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "２つの特徴をを確認するために`Pandas`の`plot()`を使ってヒストグラムを描いてみよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dfwn.plot.hist(bins=30)\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "概ね`0`を中心に左右対象に動いている。即ち，平均`0`を反映している。また，`0`から離れている観測値が少ないことが分かる。これは`0`方向に戻ることを示しており，分散が一定となるためである。この性質は`n`を`500`や`1000`などの大きな数字に設定するより一層分かりやすいだろう。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true,
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "### 自己共分散"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "`1`期違いの自己共分散$\\sigma_{\\varepsilon_t \\varepsilon_{t-1}}$を計算するために，`dfwn`の列`WN`を`1`期シフトさせた新たな列`WNlag`を作成しよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "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>WN</th>\n",
       "      <th>WNlag</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.496247</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.003145</td>\n",
       "      <td>-0.496247</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.406960</td>\n",
       "      <td>0.003145</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.092394</td>\n",
       "      <td>-0.406960</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.504291</td>\n",
       "      <td>-0.092394</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         WN     WNlag\n",
       "0 -0.496247       NaN\n",
       "1  0.003145 -0.496247\n",
       "2 -0.406960  0.003145\n",
       "3 -0.092394 -0.406960\n",
       "4  0.504291 -0.092394"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfwn['WNlag'] = dfwn['WN'].shift()\n",
    "dfwn.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`WNlag`の値は`WN`の値が`1`期シフトしていることが分かる。\n",
    "`0`番目の行の`WN`が初期値であり、同じ値が`1`番目の行の`WNlag`に入っている。\n",
    "即ち、`1`番目の行を見ると`WN`には`1`期の値、、`WNlag`には初期（`0`期）の値がある。\n",
    "同様に、各行の`WN`には`t`期の値、`WN`に`t-1`期の値が入っている。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "この２つの列を使って散布図を描いてみる。`Pandas`の`plot()`で横軸・縦軸を指定し，引数`kind`で散布図を指定するだけである。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dfwn.plot.scatter(x='WNlag', y='WN')\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "自己共分散がゼロであれば，ランダムに散らばっているはずであり，何らかのパターンも確認できないはずである。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "ここで異なるプロットの方法を紹介する。`Pandas`のサブパッケージ`plotting`にある`lag_plot()`関数を使うと共分散の強さを示す図を簡単に作成することが可能となる。\n",
    "* 必須の引数：１つの列\n",
    "* オプションの引数：`lag`は時間ラグ（デフォルトは`1`）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.plotting.lag_plot(dfwn['WN'])\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "* 横軸：`t`期の値\n",
    "* 縦軸：`t+1`期の値\n",
    "\n",
    "２つの図は同じであることが確認できる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "分散・自己共分散を計算してみよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "hidden": true
   },
   "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>WN</th>\n",
       "      <th>WNlag</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>WN</th>\n",
       "      <td>1.044167</td>\n",
       "      <td>-0.030737</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>WNlag</th>\n",
       "      <td>-0.030737</td>\n",
       "      <td>1.035711</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             WN     WNlag\n",
       "WN     1.044167 -0.030737\n",
       "WNlag -0.030737  1.035711"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfwn.cov()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "左上と右下の対角線上にあるのは、`WN`と`WNlag`の不偏分散であり、`1`に近い値となっている。両変数は標準正規分布（分散`1`）から生成したためであり、`1`にならないのはサンプルの誤差である。（`WN`と`WNlag`の不偏分散は異なるが、その理由は？）一方、右上と左下の値（同じ値となる）が**自己共分散**であり、非常に小さな値であるが、自己共分散は`0`という仮定を反映している。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "### 自己相関係数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "メソッド`.corr()`を自己相関係数を計算しよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "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>WN</th>\n",
       "      <th>WNlag</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>WN</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.029418</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>WNlag</th>\n",
       "      <td>-0.029418</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             WN     WNlag\n",
       "WN     1.000000 -0.029418\n",
       "WNlag -0.029418  1.000000"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfwn.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "右上もしくは左下にある値が自己相関係数になる。\n",
    "\n",
    "もしちろん、列`WN`を抽出し，メソッド`autocorr()`を使って自己相関係数を計算することも可能である。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "hidden": true,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.02941830514281287"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfwn['WN'].autocorr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "また，`dfwn.cov()`を使って自己相関係数を計算することができるが、上でも説明した点に注意する必要がある。`dfwn`の`0`行目には欠損値があるため、自己共分散を計算する際にその行は使われていない。同様に、自己相関係数を計算する際は欠損値がある行を使わずに計算する必要がある。この点に注意して、次のコードで計算することができる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.02941830514281287"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vcov = dfwn.dropna().cov()\n",
    "vcov.iloc[0,1] / ( vcov.iloc[0,0]**0.5 * vcov.iloc[1,1]**0.5 )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true,
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "## 自己回帰モデル：AR(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "GDPや構成要素を含め、マクロ変数の重要な特徴は持続性（正の自己相関係数）である。\n",
    "この点については次章で確認するが，その基本となる統計的モデルである自己回帰モデルを考察し、それを出発点として景気循環の議論を進めていく事にする。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true,
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "### 説明"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "ここでは持続性を捉える確率過程である自己回帰モデルを考える。英語で**A**ugo**r**egressive Modelと呼ばれ，AR(1)と表記され，次式で表される。（AR(1)の`(1)`は右辺と左辺の変数は１期しか違わないことを表している。）\n",
    "\n",
    "$$\n",
    "y_t=\\rho y_{t-1}+\\varepsilon_t\n",
    "$$ (eq:13-ar1)\n",
    "\n",
    "ここで\n",
    "* $y_t$：$t$期の$y$の値\n",
    "* $-1<\\rho<1$\n",
    "* $\\varepsilon_t\\sim WN(0,\\sigma^2)$（ホワイト・ノイズ）\n",
    "\n",
    "次の特徴がある。第一に、$\\varepsilon_t$を所与とすると$y_t$の差分方程式となっている。$-1<\\rho<1$となっているため，安定的な過程であることがわかる。即ち，$\\varepsilon_t=0$であれば、$y_t$は定常状態である$0$に近づいて行くことになる。しかしホワイト・ノイズである$\\varepsilon_t$により、毎期確率的なショックが発生し$y_t$を定常状態から乖離させることになる。第二に、今期の値$y_t$は前期の値$y_{t-1}$に依存しており，その依存度はパラメータ$\\rho$によって決定される。この$\\rho$こそが$y_t$の持続性の強さを決定することになり，自己回帰モデル[](eq:13-ar1)の自己相関係数は$\\rho$と等しくなる。即ち、持続性を捉えるためには、$\\rho\\ne 0$が必須である。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ここで考えるAR(1)の特徴をまとめておこう。\n",
    "1. $y_t$の確率分布が変化しない定常過程 \n",
    "1. 平均は一定：$\\quad\\text{E}\\left[y_t\\right]=0$\n",
    "1. 分散は一定：$\\text{E}\\left[y_t^2\\right]=\\dfrac{\\sigma^2}{1-\\rho^2}$（$t$の添字はない）\n",
    "1. 自己共分散は一定：$\\text{E}\\left[y_t y_{t-s}\\right]=\\sigma_{y_t y_{t-s}}^2=\\rho^s\\dfrac{\\sigma^2}{1-\\rho^2}$（$s\\ne 0$）。従って，\n",
    "\n",
    "    $$\n",
    "    \\text{自己相関関数}(s)=\\frac{\\sigma_{y_t y_{t-s}}^2}\n",
    "                           {\\sigma_{y_t}\\times\\sigma_{y_{t-s}}}\n",
    "                           =\\rho^s\n",
    "    $$\n",
    "   であり，$s=1$の自己相関係数は$\\rho$となる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true,
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "### ３つの例：持続性の違い"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "直観的にマクロ変数の特徴である持続性とは，前期の値が今期の値にどれだけ影響を持っているかを示す。$\\rho$の値を変えて持続性の違いを視覚的に確認するための関数を作成しよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "def ar1_model(rho, y0=0, T=100):\n",
    "    \"\"\"引数：\n",
    "            rho: AR(1)の持続性を捉えるパラメータ\n",
    "            y0:  初期値\n",
    "            T:   シミュレーションの回数（デフォルト：0）\n",
    "       戻り値：\n",
    "            matplotlibの図を示す\n",
    "            自己相関係数の値を表示する\"\"\"\n",
    "    \n",
    "    y = y0                          #1\n",
    "    y_lst = [y]                     #2\n",
    "\n",
    "    for t in range(1,T):            #3\n",
    "        e = rng.normal()            #4\n",
    "        y = rho*y + e               #5\n",
    "        y_lst.append(y)            #6\n",
    "\n",
    "    df_ar1 = pd.Series(y_lst)      #7\n",
    "\n",
    "    ac = df_ar1.autocorr()          #8\n",
    "    \n",
    "    ax_ = df_ar1.plot(marker='.')   #9\n",
    "    ax_.set_title(fr'$\\rho$={rho}　　自己相関係数：{ac:.3f}',size=20) #10\n",
    "    ax_.axhline(0, c='red')         #11"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "```{admonition} コードの説明\n",
    ":class: dropdown\n",
    "\n",
    "* `#1`：`for`ループで使うアップデート用の`y`であり，初期値を割り当てている。\n",
    "* `#2`：`y`の値を格納するリスト。初期値を入れてある。\n",
    "* `#3`：`T`期間の`for`ループの開始。変数`t`は(4)と(5)に入っていないので単にループの回数を数えている。\n",
    "    * `range(1,T)`の`1`はループの計算が$t=1$期の`y`の計算から始まるため。$t=0$期の`y`は(1)で与えられている。\n",
    "* `#4`：`t`期のホワイト・ノイズの生成。\n",
    "* `#5`：右辺の`e`は`t`期のホワイトノイズであり，`y`前期の`y`となっている。\n",
    "* `#6`：`y_list`に`y`を追加。\n",
    "* `#7`：`y_list`を使って`Series`を作成し`df_ar1`に割り当てる。\n",
    "* `#8`：`.autocorr()`を使い己相関係数を計算し`ac`に割り当てる。\n",
    "* `#9`：`y`のプロット\n",
    "    * `marker='.'`はデータのマーカーを点に設定。\n",
    "    * 図の「軸」を`ax_`に割り当てる。\n",
    "* `#10`：図のタイトルの設定\n",
    "    * `fr`の`f`は`f-string`を表し，`{rho}`と`{ac:.3f}`に数値を代入する。`:.3f`は小数点第三位までの表示を設定\n",
    "    * `fr`の`r`は`$\\rho$`をギリシャ文字に変換するためののも。`$\\rho$`は[LaTeX](https://ja.wikipedia.org/wiki/LaTeX)のコード。\n",
    "* `#11`：`.axhline()`は横線をひくメソッド。\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ar1_model(0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "この例では$\\rho$の値が低いため，$y$は定常状態の0に直ぐに戻ろうとする力が強い。従って、前期の値の今期の値に対する影響力が小さいため、持続性が低い。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ar1_model(0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "$\\rho$の値が高くなると、定常状態の$0$に戻ろうとする作用が弱くなり、持続性が強くなることがわかる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ar1_model(0.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "$\\rho$が非常に高いため、持続性も非常に強くなっている。即ち、今期の値は前期の値に対する依存度が大きい。"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}