resample()
2019-01-01
10
- 7.068212
+ 5.277740
2019-02-01
20
- 5.507801
+ 5.179652
2019-03-01
30
- 4.659180
+ 6.903653
2019-04-01
40
- 6.750383
+ 5.135640
2019-05-01
50
- 5.770613
+ 5.288257
2019-06-01
60
- 5.057649
+ 5.916110
2019-07-01
70
- 5.291954
+ 3.649450
2019-08-01
80
- 5.090206
+ 5.648054
2019-09-01
90
- 5.229165
+ 5.053249
2019-10-01
100
- 4.371847
+ 3.050738
2019-11-01
110
- 5.835155
+ 5.287720
2019-12-01
120
- 6.839144
+ 4.231305
2020-01-01
10
- 3.745913
+ 4.562625
2020-02-01
20
- 4.395061
+ 5.890086
2020-03-01
30
- 6.024376
+ 3.438143
2020-04-01
40
- 6.345998
+ 4.802732
2020-05-01
50
- 3.855593
+ 4.888795
2020-06-01
60
- 3.339227
+ 4.790555
2020-07-01
70
- 5.439351
+ 4.667200
2020-08-01
80
- 5.569649
+ 5.209155
2020-09-01
90
- 6.225637
+ 5.379132
2020-10-01
100
- 5.086193
+ 5.970429
2020-11-01
110
- 3.244917
+ 4.291284
2020-12-01
120
- 4.087981
+ 5.559605
@@ -766,7 +766,7 @@ resample()
-<pandas.core.resample.DatetimeIndexResampler object at 0x107bf6b40>
+<pandas.core.resample.DatetimeIndexResampler object at 0x10f1fe6f0>
@@ -807,42 +807,42 @@ resample()
2019-01-01
20.0
- 5.745064
+ 5.787015
2019-04-01
50.0
- 5.859548
+ 5.446669
2019-07-01
80.0
- 5.203775
+ 4.783584
2019-10-01
110.0
- 5.682049
+ 4.189921
2020-01-01
20.0
- 4.721784
+ 4.630285
2020-04-01
50.0
- 4.513606
+ 4.827361
2020-07-01
80.0
- 5.744879
+ 5.085162
2020-10-01
110.0
- 4.139697
+ 5.273773
@@ -883,12 +883,12 @@ resample()
2019-01-01
65.0
- 5.622609
+ 5.051797
2020-01-01
65.0
- 4.779991
+ 4.954145
@@ -973,12 +973,12 @@ resample()
2019-01-01
0.5547
- 0.154317
+ 0.201180
2020-01-01
0.5547
- 0.237913
+ 0.143355
@@ -1638,7 +1638,7 @@ 変化率の計算
-<pandas.core.groupby.generic.DataFrameGroupBy object at 0x1136ebfe0>
+<pandas.core.groupby.generic.DataFrameGroupBy object at 0x1181ab740>
@@ -1653,7 +1653,7 @@ 変化率の計算
-<pandas.core.groupby.generic.SeriesGroupBy object at 0x113cbbd70>
+<pandas.core.groupby.generic.SeriesGroupBy object at 0x1181cd280>
diff --git a/13a_Random_Variables.html b/13a_Random_Variables.html
index af71e3cd..8cefe07a 100644
--- a/13a_Random_Variables.html
+++ b/13a_Random_Variables.html
@@ -659,53 +659,53 @@ .cov
0
- 9.226527
- 59.884129
+ 9.986898
+ 65.226378
1
- 8.447087
- 10.864864
+ 10.950868
+ 25.126103
2
- 9.089684
- 98.844441
+ 8.616695
+ 91.922990
3
- 9.307079
- 30.984169
+ 9.438771
+ 2.279898
4
- 10.704744
- 79.099151
+ 10.677754
+ 19.288365
5
- 9.598606
- 55.097851
+ 10.055099
+ 23.828399
6
- 9.372898
- 8.376976
+ 9.469716
+ 89.078437
7
- 8.954774
- 73.010548
+ 9.359286
+ 24.031391
8
- 10.789657
- 65.658884
+ 9.010822
+ 31.161343
9
- 9.109282
- 35.203200
+ 11.323700
+ 29.797652
@@ -746,13 +746,13 @@ .cov
X
- 0.551495
- 8.565577
+ 0.766032
+ -11.157834
Y
- 8.565577
- 882.945539
+ -11.157834
+ 945.832728
@@ -795,11 +795,11 @@ .cov
X
1.000000
- 0.388167
+ -0.414524
Y
- 0.388167
+ -0.414524
1.000000
@@ -816,7 +816,7 @@ .cov
-0.38816740703052205
+-0.4145235186574958
@@ -1019,53 +1019,53 @@ .cov()
0
- 10.743490
+ 8.268658
NaN
1
- 11.515666
- 10.743490
+ 9.506594
+ 8.268658
2
- 11.058309
- 11.515666
+ 10.519143
+ 9.506594
3
- 9.699965
- 11.058309
+ 10.633746
+ 10.519143
4
- 10.317081
- 9.699965
+ 10.210946
+ 10.633746
5
- 8.613991
- 10.317081
+ 11.047005
+ 10.210946
6
- 11.934332
- 8.613991
+ 10.337397
+ 11.047005
7
- 11.172057
- 11.934332
+ 11.335130
+ 10.337397
8
- 10.105710
- 11.172057
+ 8.454739
+ 11.335130
9
- 10.341831
- 10.105710
+ 9.659399
+ 8.454739
@@ -1114,13 +1114,13 @@ .cov()
X
- 0.921925
- -0.137977
+ 1.050337
+ 0.061156
X_lag
- -0.137977
- 1.031133
+ 0.061156
+ 1.165773
@@ -1165,11 +1165,11 @@ .cov()
X
1.000000
- -0.133756
+ 0.064691
X_lag
- -0.133756
+ 0.064691
1.000000
@@ -1186,7 +1186,7 @@ .cov()
--0.133756232065724
+0.06469054006502663
@@ -1203,7 +1203,7 @@ .cov()
--0.133756232065724
+0.06469054006502663
@@ -1277,8 +1277,8 @@ 平均と分散
-array([5.99572137, 6.01985899, 4.28637238, 4.18736439, 5.03320963,
- 8.3873237 , 7.7770293 , 8.10349139, 7.5331098 , 4.70405868])
+array([3.99688835, 7.35944867, 4.80803364, 9.79589432, 5.00834094,
+ 5.32001356, 5.13081879, 3.75959095, 5.22039544, 5.39445347])
@@ -1302,7 +1302,7 @@ 平均と分散
-
+
２つの特徴がある。
@@ -1318,7 +1318,7 @@ 平均と分散
-(0.04193280260752992, 0.9610707122130532)
+(0.13031856002176803, 1.0106524139014506)
@@ -1333,7 +1333,7 @@ 平均と分散
-
+
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。
@@ -1374,28 +1374,28 @@ 自己共分散
-
+
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。
@@ -1431,7 +1431,7 @@ 自己共分散
-
+
@@ -1472,13 +1472,13 @@ 自己共分散
-0.2570667340828474
+-0.005097087246679094
@@ -1556,7 +1556,7 @@ 自己相関係数
-0.25706673408284736
+-0.005097087246679093
@@ -1667,7 +1667,7 @@ ３つの例：持続性の違い
-
+
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。
@@ -1678,7 +1678,7 @@ ３つの例：持続性の違い
-
+
\(\rho\)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。
@@ -1689,7 +1689,7 @@ ３つの例：持続性の違い
-
+
\(\rho\)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。
diff --git a/13b_Stochastic_Solow.html b/13b_Stochastic_Solow.html
index 6990f05b..595b372d 100644
--- a/13b_Stochastic_Solow.html
+++ b/13b_Stochastic_Solow.html
@@ -1094,10 +1094,10 @@ TFP#
-TFPの自己相関係数：0.663
+TFPの自己相関係数：0.535
-
+
シミュレーションを行う度に図と自己相関係数は異なることになる。
@@ -1612,95 +1612,95 @@ 実行#<
8.500577e+05
1.000000
0.366461
- 272210.617761
- 213095.442439
+ 2.722106e+05
+ 2.130954e+05
59115.175322
- 13.704888
- -5.182883
- 0.083737
- -8.373726
- 12.616727
- -10.239564
- 12.371891
- -10.239564
- 11.089639
- -10.239564
+ 13.780344
+ -12.728463
+ 0.073138
+ -7.313825
+ 12.633292
+ -11.896071
+ 12.388456
+ -11.896071
+ 11.106204
+ -11.896071
1
8.879214e+05
- 0.956201
+ 0.521533
0.367346
- 265042.428091
- 207483.947333
- 57558.480757
- 13.760500
- -6.386177
- 0.086970
- -13.175700
- 12.642392
- -15.474724
- 12.397556
- -15.474724
- 11.115304
- -15.474724
+ 1.445601e+05
+ 1.131664e+05
+ 31393.688704
+ 13.836467
+ -13.982835
+ 0.080885
+ -73.186687
+ 12.663656
+ -78.220508
+ 12.418820
+ -78.220508
+ 11.136567
+ -78.220508
2
- 9.232819e+05
- 3.177727
+ 8.971171e+05
+ 7.485312
0.368233
- 895439.064586
- 700979.209461
- 194459.855125
- 13.816080
- -8.039004
- 0.090150
- 106.601600
- 12.667994
- 103.707559
- 12.423158
- 103.707559
- 11.140905
- 103.707559
+ 2.087540e+06
+ 1.634195e+06
+ 453344.817356
+ 13.892510
+ -18.556844
+ 0.088586
+ 192.435649
+ 12.693945
+ 185.755185
+ 12.449109
+ 185.755185
+ 11.166856
+ 185.755185
3
- 1.094660e+06
- 3.142032
+ 1.328034e+06
+ 1.544094
0.369123
- 943621.976175
- 738698.380549
- 204923.595627
- 13.871555
- 3.439931
- 0.093143
- 105.172659
- 12.693371
- 106.411034
- 12.448535
- 106.411034
- 11.166282
- 106.411034
+ 4.971370e+05
+ 3.891752e+05
+ 107961.777870
+ 13.948307
+ 15.090339
+ 0.095738
+ 33.869922
+ 12.723597
+ 39.302444
+ 12.478761
+ 39.302444
+ 11.196508
+ 39.302444
4
- 1.272217e+06
- 1.718926
+ 1.402795e+06
+ 0.725768
0.370015
- 546252.979147
- 427624.834154
- 118628.144993
- 13.926802
- 12.946903
- 0.096481
- 44.521859
- 12.719010
- 49.182744
- 12.474174
- 49.182744
- 11.191922
- 49.182744
+ 2.388969e+05
+ 1.870163e+05
+ 51880.526247
+ 14.003574
+ 15.040307
+ 0.103041
+ -42.356623
+ 12.753208
+ -36.942112
+ 12.508372
+ -36.942112
+ 11.226120
+ -36.942112
@@ -1716,7 +1716,7 @@ 実行#<
-
+
トレンドの傾きは成長率を表しているが，徐々に減少していることが分かる。最初は成長率に対する資本蓄積の効果が大きいが，定常状態に近づくにつれて資本蓄積の効果が減少しているためである。
@@ -1730,7 +1730,7 @@ 実行#<
-
+
絶対値で概ね2％内に収まった変動となっている。データでは，リーマンショック時はマイナス約4％程乖離したが，それ以外は絶対値で2％以内に収まっており，シミュレーションは概ねデータと同じような特徴を持っていると言える。
@@ -1754,11 +1754,11 @@ 結果１：自己相関
--- シミュレーション：変動の自己相関係数 ---
-Yの変動： 0.395
-Cの変動： 0.395
-Iの変動： 0.395
-Kの変動： 0.828
-Aの変動： 0.394
+Yの変動： 0.538
+Cの変動： 0.538
+Iの変動： 0.538
+Kの変動： 0.901
+Aの変動： 0.532
@@ -1842,8 +1842,8 @@ 結果２：GDPとの相関\(h\)
の推定値
Model: OLS Adj. R-squared: 0.688
Method: Least Squares F-statistic: 384.1
Date: Fri, 03 Jan 2025 Prob (F-statistic): 8.56e-46
-Time: 01:09:49 Log-Likelihood: 716.66
+Time: 01:30:09 Log-Likelihood: 716.66
No. Observations: 175 AIC: -1429.
Df Residuals: 173 BIC: -1423.
Df Model: 1
@@ -1348,7 +1348,7 @@ 最初のスイッチ：\(c\)残差の自己相関の検定
-\(H_0\)：残差は独立分布（無相関）
\(H_A\)：\(\rho_{p}\ne0\)
\(H_0\)：残差は独立分布
\(H_A\)：残差は独立分布ではない
+
\(u_t\)と\(v_t\)が毎期毎期変動しており，その結果として\(p_t\)と\(y_t\)が変動していることになる。
@@ -1095,7 +1095,7 @@
プロット
-
+
このプロットから次の点を確認できる。
@@ -1149,8 +1149,8 @@ GDPと価格水準の乖離率の標準偏差
-yの標準偏差:0.01375
-pの標準偏差:0.01415
+yの標準偏差:0.01379
+pの標準偏差:0.01421
@@ -1200,8 +1200,8 @@ 自己相関係数
-y:0.043
-p:0.819
+y:0.049
+p:0.821
@@ -1247,7 +1247,7 @@ p
--0.10826051696903893
+-0.11107441089736105
@@ -1278,11 +1278,11 @@ 結果のまとめと拡張-0.15298
WNショック
0.01375
0.01415
0.04270
0.81852
-0.10826
0.01379
0.01421
0.04869
0.82093
-0.11107
AR(1)ショック
0.01252
\(p_t\)に対する影響
需要ショックと供給ショックに起因する\(p_t\)の変動の割合を計算するために，式(144)の両辺を\(\text{Var}(p_{t})\)で割ると次式となる。
-
-(145)#\[\begin{align}
+
+(145)#\[\begin{align}
1&=
\frac{(ah)^2}{1-h^2}\cdot\frac{\text{Var}(u_{t})}{\text{Var}(p_{t})}
+\frac{h^2}{1-h^2}\cdot\frac{\text{Var}(v_{t})}{\text{Var}(p_{t})}
@@ -1580,8 +1580,8 @@ \(y_t\)に対する影響
\(p_t\)の総変動の大きさ（水準）を決定する上で，\(h\) が重要な役割を果たしている。\(h\)はは約0.8であり\(p_t\)の高い持続性を意味する。持続性が高い場合，一旦総供給曲線が定常状態の位置から離れると元の位置に戻るには時間が掛かることになる。即ち，定常状態から離れた状態が長くなる。そのような状況下で，更にショックが発生すると，定常状態から更に乖離する結果につながることになり，変動が増幅されることになる。その効果が\(\dfrac{h^2}{1-h^2}\)で捉えられている。
需要ショックと供給ショックに起因する\(y_t\)の変動の割合を計算するために，式(150)の両辺を\(\text{Var}(y_{t})\)で割ると次式となる。
-
-(151)#\[\begin{align}
+
+(151)#\[\begin{align}
1
&=\frac{h^2}{1-h^2}2ach\frac{\text{Var}(u_{t})}{\text{Var}(y_{t})}
+\frac{h^2}{1-h^2}c^2\frac{\text{Var}(v_{t})}{\text{Var}(y_{t})}\\
@@ -1814,8 +1814,8 @@ 付録#<
付録Ｂ：式(150)の導出#
-
-(152)#\[\begin{align}
+
+(152)#\[\begin{align}
\text{Var}(y_{t})
&=(ch)^2\text{Var}(p_{t})+\text{Var}(e_{yt})\\
&=(ch)^2\left[
@@ -1839,8 +1839,8 @@ 付録#<
+\frac{(ch)^2}{1-h^2}\text{Var}(v_{t})
\end{align}\]
ここで
-
-(153)#\[\begin{align}
+
+(153)#\[\begin{align}
1+(ach)^2-h^2
&=1+h^2[(ac)^2-1]=1+\frac{(ac)^2-1}{(1+ac)^2}\\
&=1+\frac{(ac+1)(ac-1)}{(1+ac)^2}=1+\frac{ac-1}{1+ac}\\
@@ -1852,8 +1852,8 @@ 付録#<
付録Ｃ：式(u-y)と(v-y)の導出#
式(u-y)に式(150)を代入して整理する。
-
-(154)#\[\begin{align}
+
+(154)#\[\begin{align}
\left[
\begin{split}
&y_t\text{の変動に対する}\\
@@ -1880,8 +1880,8 @@ 付録#<
\tag{u-y}
\end{align}\]
同様に式(v-y)に式(150)を代入して整理する。
-
-(155)#\[\begin{align}
+
+(155)#\[\begin{align}
\left[
\begin{split}
&p_t\text{の変動に対する}\\
diff --git a/6_Regression.html b/6_Regression.html
index bf5f3ada..9b05fb5c 100644
--- a/6_Regression.html
+++ b/6_Regression.html
@@ -611,7 +611,7 @@ 回帰分析#
Model: OLS Adj. R-squared: 0.848
Method: Least Squares F-statistic: 336.7
Date: Fri, 03 Jan 2025 Prob (F-statistic): 4.64e-26
-Time: 01:10:19 Log-Likelihood: 49.767
+Time: 01:30:30 Log-Likelihood: 49.767
No. Observations: 61 AIC: -95.53
Df Residuals: 59 BIC: -91.31
Df Model: 1
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diff --git a/_sources/18_ADAS-1.ipynb b/_sources/18_ADAS-1.ipynb
index 768981cf..cb024c4b 100644
--- a/_sources/18_ADAS-1.ipynb
+++ b/_sources/18_ADAS-1.ipynb
@@ -1629,8 +1629,8 @@
"\n",
"＜帰無仮説＞\n",
"\n",
- "* $H_0$：残差は独立分布（無相関）\n",
- "* $H_A$：$\\rho_{p}\\ne0$"
+ "* $H_0$：残差は独立分布\n",
+ "* $H_A$：残差は独立分布ではない"
]
},
{
@@ -1799,7 +1799,9 @@
},
{
"cell_type": "markdown",
- "metadata": {},
+ "metadata": {
+ "jp-MarkdownHeadingCollapsed": true
+ },
"source": [
"(sec:18-1-appendix_B)=\n",
"### 付録Ｂ"
diff --git a/_sources/index.ipynb b/_sources/index.ipynb
index 37b33d95..bca03462 100644
--- a/_sources/index.ipynb
+++ b/_sources/index.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "9515b5c2",
+ "id": "fb39b6c9",
"metadata": {},
"source": [
"# Pythonで学ぶマクロ経済学 (中級＋レベル)\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": 1,
- "id": "f0488bae",
+ "id": "aab734a9",
"metadata": {},
"outputs": [
{
@@ -41,7 +41,7 @@
},
{
"cell_type": "markdown",
- "id": "bf66ad96",
+ "id": "35f57f40",
"metadata": {},
"source": [
"
resample()
-<pandas.core.resample.DatetimeIndexResampler object at 0x107bf6b40>
+<pandas.core.resample.DatetimeIndexResampler object at 0x10f1fe6f0>
@@ -807,42 +807,42 @@ resample()
2019-01-01
20.0
- 5.745064
+ 5.787015
2019-04-01
50.0
- 5.859548
+ 5.446669
2019-07-01
80.0
- 5.203775
+ 4.783584
2019-10-01
110.0
- 5.682049
+ 4.189921
2020-01-01
20.0
- 4.721784
+ 4.630285
2020-04-01
50.0
- 4.513606
+ 4.827361
2020-07-01
80.0
- 5.744879
+ 5.085162
2020-10-01
110.0
- 4.139697
+ 5.273773
@@ -883,12 +883,12 @@ resample()
2019-01-01
65.0
- 5.622609
+ 5.051797
2020-01-01
65.0
- 4.779991
+ 4.954145
@@ -973,12 +973,12 @@ resample()
2019-01-01
0.5547
- 0.154317
+ 0.201180
2020-01-01
0.5547
- 0.237913
+ 0.143355
@@ -1638,7 +1638,7 @@ 変化率の計算
-<pandas.core.groupby.generic.DataFrameGroupBy object at 0x1136ebfe0>
+<pandas.core.groupby.generic.DataFrameGroupBy object at 0x1181ab740>
@@ -1653,7 +1653,7 @@ 変化率の計算
-<pandas.core.groupby.generic.SeriesGroupBy object at 0x113cbbd70>
+<pandas.core.groupby.generic.SeriesGroupBy object at 0x1181cd280>
diff --git a/13a_Random_Variables.html b/13a_Random_Variables.html
index af71e3cd..8cefe07a 100644
--- a/13a_Random_Variables.html
+++ b/13a_Random_Variables.html
@@ -659,53 +659,53 @@ .cov
0
- 9.226527
- 59.884129
+ 9.986898
+ 65.226378
1
- 8.447087
- 10.864864
+ 10.950868
+ 25.126103
2
- 9.089684
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3
- 9.307079
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4
- 10.704744
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5
- 9.598606
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6
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- 8.954774
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- 65.658884
+ 9.010822
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9
- 9.109282
- 35.203200
+ 11.323700
+ 29.797652
@@ -746,13 +746,13 @@ .cov
X
- 0.551495
- 8.565577
+ 0.766032
+ -11.157834
Y
- 8.565577
- 882.945539
+ -11.157834
+ 945.832728
@@ -795,11 +795,11 @@ .cov
X
1.000000
- 0.388167
+ -0.414524
Y
- 0.388167
+ -0.414524
1.000000
@@ -816,7 +816,7 @@ .cov
-0.38816740703052205
+-0.4145235186574958
@@ -1019,53 +1019,53 @@ .cov()
0
- 10.743490
+ 8.268658
NaN
1
- 11.515666
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+ 8.268658
2
- 11.058309
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- 8.613991
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- 11.934332
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- 11.172057
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+ 11.335130
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- 10.105710
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+ 8.454739
+ 11.335130
9
- 10.341831
- 10.105710
+ 9.659399
+ 8.454739
@@ -1114,13 +1114,13 @@ .cov()
X
- 0.921925
- -0.137977
+ 1.050337
+ 0.061156
X_lag
- -0.137977
- 1.031133
+ 0.061156
+ 1.165773
@@ -1165,11 +1165,11 @@ .cov()
X
1.000000
- -0.133756
+ 0.064691
X_lag
- -0.133756
+ 0.064691
1.000000
@@ -1186,7 +1186,7 @@ .cov()
--0.133756232065724
+0.06469054006502663
@@ -1203,7 +1203,7 @@ .cov()
--0.133756232065724
+0.06469054006502663
@@ -1277,8 +1277,8 @@ 平均と分散
-array([5.99572137, 6.01985899, 4.28637238, 4.18736439, 5.03320963,
- 8.3873237 , 7.7770293 , 8.10349139, 7.5331098 , 4.70405868])
+array([3.99688835, 7.35944867, 4.80803364, 9.79589432, 5.00834094,
+ 5.32001356, 5.13081879, 3.75959095, 5.22039544, 5.39445347])
@@ -1302,7 +1302,7 @@ 平均と分散
-
+
２つの特徴がある。
@@ -1318,7 +1318,7 @@ 平均と分散
-(0.04193280260752992, 0.9610707122130532)
+(0.13031856002176803, 1.0106524139014506)
@@ -1333,7 +1333,7 @@ 平均と分散
-
+
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。
@@ -1374,28 +1374,28 @@ 自己共分散
-
+
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。
@@ -1431,7 +1431,7 @@ 自己共分散
-
+
@@ -1472,13 +1472,13 @@ 自己共分散
-0.2570667340828474
+-0.005097087246679094
@@ -1556,7 +1556,7 @@ 自己相関係数
-0.25706673408284736
+-0.005097087246679093
@@ -1667,7 +1667,7 @@ ３つの例：持続性の違い
-
+
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。
@@ -1678,7 +1678,7 @@ ３つの例：持続性の違い
-
+
\(\rho\)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。
@@ -1689,7 +1689,7 @@ ３つの例：持続性の違い
-
+
\(\rho\)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。
diff --git a/13b_Stochastic_Solow.html b/13b_Stochastic_Solow.html
index 6990f05b..595b372d 100644
--- a/13b_Stochastic_Solow.html
+++ b/13b_Stochastic_Solow.html
@@ -1094,10 +1094,10 @@ TFP#
-TFPの自己相関係数：0.663
+TFPの自己相関係数：0.535
-
+
シミュレーションを行う度に図と自己相関係数は異なることになる。
@@ -1612,95 +1612,95 @@ 実行#<
8.500577e+05
1.000000
0.366461
- 272210.617761
- 213095.442439
+ 2.722106e+05
+ 2.130954e+05
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@@ -1716,7 +1716,7 @@ 実行#<
-
+
トレンドの傾きは成長率を表しているが，徐々に減少していることが分かる。最初は成長率に対する資本蓄積の効果が大きいが，定常状態に近づくにつれて資本蓄積の効果が減少しているためである。
@@ -1730,7 +1730,7 @@ 実行#<
-
+
絶対値で概ね2％内に収まった変動となっている。データでは，リーマンショック時はマイナス約4％程乖離したが，それ以外は絶対値で2％以内に収まっており，シミュレーションは概ねデータと同じような特徴を持っていると言える。
@@ -1754,11 +1754,11 @@ 結果１：自己相関
--- シミュレーション：変動の自己相関係数 ---
-Yの変動： 0.395
-Cの変動： 0.395
-Iの変動： 0.395
-Kの変動： 0.828
-Aの変動： 0.394
+Yの変動： 0.538
+Cの変動： 0.538
+Iの変動： 0.538
+Kの変動： 0.901
+Aの変動： 0.532
@@ -1842,8 +1842,8 @@ 結果２：GDPとの相関\(h\)
の推定値
Model: OLS Adj. R-squared: 0.688
Method: Least Squares F-statistic: 384.1
Date: Fri, 03 Jan 2025 Prob (F-statistic): 8.56e-46
-Time: 01:09:49 Log-Likelihood: 716.66
+Time: 01:30:09 Log-Likelihood: 716.66
No. Observations: 175 AIC: -1429.
Df Residuals: 173 BIC: -1423.
Df Model: 1
@@ -1348,7 +1348,7 @@ 最初のスイッチ：\(c\)残差の自己相関の検定
-\(H_0\)：残差は独立分布（無相関）
\(H_A\)：\(\rho_{p}\ne0\)
\(H_0\)：残差は独立分布
\(H_A\)：残差は独立分布ではない
\(u_t\)と\(v_t\)が毎期毎期変動しており，その結果として\(p_t\)と\(y_t\)が変動していることになる。
@@ -1095,7 +1095,7 @@
プロット
-
+
このプロットから次の点を確認できる。
@@ -1149,8 +1149,8 @@ GDPと価格水準の乖離率の標準偏差
-yの標準偏差:0.01375
-pの標準偏差:0.01415
+yの標準偏差:0.01379
+pの標準偏差:0.01421
@@ -1200,8 +1200,8 @@ 自己相関係数
-y:0.043
-p:0.819
+y:0.049
+p:0.821
@@ -1247,7 +1247,7 @@ p
--0.10826051696903893
+-0.11107441089736105
@@ -1278,11 +1278,11 @@ 結果のまとめと拡張-0.15298
WNショック
0.01375
0.01415
0.04270
0.81852
-0.10826
0.01379
0.01421
0.04869
0.82093
-0.11107
AR(1)ショック
0.01252
\(p_t\)に対する影響
需要ショックと供給ショックに起因する\(p_t\)の変動の割合を計算するために，式(144)の両辺を\(\text{Var}(p_{t})\)で割ると次式となる。
-
-(145)#\[\begin{align}
+
+(145)#\[\begin{align}
1&=
\frac{(ah)^2}{1-h^2}\cdot\frac{\text{Var}(u_{t})}{\text{Var}(p_{t})}
+\frac{h^2}{1-h^2}\cdot\frac{\text{Var}(v_{t})}{\text{Var}(p_{t})}
@@ -1580,8 +1580,8 @@ \(y_t\)に対する影響
\(p_t\)の総変動の大きさ（水準）を決定する上で，\(h\) が重要な役割を果たしている。\(h\)はは約0.8であり\(p_t\)の高い持続性を意味する。持続性が高い場合，一旦総供給曲線が定常状態の位置から離れると元の位置に戻るには時間が掛かることになる。即ち，定常状態から離れた状態が長くなる。そのような状況下で，更にショックが発生すると，定常状態から更に乖離する結果につながることになり，変動が増幅されることになる。その効果が\(\dfrac{h^2}{1-h^2}\)で捉えられている。
需要ショックと供給ショックに起因する\(y_t\)の変動の割合を計算するために，式(150)の両辺を\(\text{Var}(y_{t})\)で割ると次式となる。
-
-(151)#\[\begin{align}
+
+(151)#\[\begin{align}
1
&=\frac{h^2}{1-h^2}2ach\frac{\text{Var}(u_{t})}{\text{Var}(y_{t})}
+\frac{h^2}{1-h^2}c^2\frac{\text{Var}(v_{t})}{\text{Var}(y_{t})}\\
@@ -1814,8 +1814,8 @@ 付録#<
付録Ｂ：式(150)の導出#
-
-(152)#\[\begin{align}
+
+(152)#\[\begin{align}
\text{Var}(y_{t})
&=(ch)^2\text{Var}(p_{t})+\text{Var}(e_{yt})\\
&=(ch)^2\left[
@@ -1839,8 +1839,8 @@ 付録#<
+\frac{(ch)^2}{1-h^2}\text{Var}(v_{t})
\end{align}\]
ここで
-
-(153)#\[\begin{align}
+
+(153)#\[\begin{align}
1+(ach)^2-h^2
&=1+h^2[(ac)^2-1]=1+\frac{(ac)^2-1}{(1+ac)^2}\\
&=1+\frac{(ac+1)(ac-1)}{(1+ac)^2}=1+\frac{ac-1}{1+ac}\\
@@ -1852,8 +1852,8 @@ 付録#<
付録Ｃ：式(u-y)と(v-y)の導出#
式(u-y)に式(150)を代入して整理する。
-
-(154)#\[\begin{align}
+
+(154)#\[\begin{align}
\left[
\begin{split}
&y_t\text{の変動に対する}\\
@@ -1880,8 +1880,8 @@ 付録#<
\tag{u-y}
\end{align}\]
同様に式(v-y)に式(150)を代入して整理する。
-
-(155)#\[\begin{align}
+
+(155)#\[\begin{align}
\left[
\begin{split}
&p_t\text{の変動に対する}\\
diff --git a/6_Regression.html b/6_Regression.html
index bf5f3ada..9b05fb5c 100644
--- a/6_Regression.html
+++ b/6_Regression.html
@@ -611,7 +611,7 @@ 回帰分析#
Model: OLS Adj. R-squared: 0.848
Method: Least Squares F-statistic: 336.7
Date: Fri, 03 Jan 2025 Prob (F-statistic): 4.64e-26
-Time: 01:10:19 Log-Likelihood: 49.767
+Time: 01:30:30 Log-Likelihood: 49.767
No. Observations: 61 AIC: -95.53
Df Residuals: 59 BIC: -91.31
Df Model: 1
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diff --git a/_images/f9e9b83dd3a04363211d9757cffe47aeb643db32d911a7fb1feaf926ad9a087a.png b/_images/f9e9b83dd3a04363211d9757cffe47aeb643db32d911a7fb1feaf926ad9a087a.png
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diff --git a/_sources/18_ADAS-1.ipynb b/_sources/18_ADAS-1.ipynb
index 768981cf..cb024c4b 100644
--- a/_sources/18_ADAS-1.ipynb
+++ b/_sources/18_ADAS-1.ipynb
@@ -1629,8 +1629,8 @@
"\n",
"＜帰無仮説＞\n",
"\n",
- "* $H_0$：残差は独立分布（無相関）\n",
- "* $H_A$：$\\rho_{p}\\ne0$"
+ "* $H_0$：残差は独立分布\n",
+ "* $H_A$：残差は独立分布ではない"
]
},
{
@@ -1799,7 +1799,9 @@
},
{
"cell_type": "markdown",
- "metadata": {},
+ "metadata": {
+ "jp-MarkdownHeadingCollapsed": true
+ },
"source": [
"(sec:18-1-appendix_B)=\n",
"### 付録Ｂ"
diff --git a/_sources/index.ipynb b/_sources/index.ipynb
index 37b33d95..bca03462 100644
--- a/_sources/index.ipynb
+++ b/_sources/index.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "9515b5c2",
+ "id": "fb39b6c9",
"metadata": {},
"source": [
"# Pythonで学ぶマクロ経済学 (中級＋レベル)\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": 1,
- "id": "f0488bae",
+ "id": "aab734a9",
"metadata": {},
"outputs": [
{
@@ -41,7 +41,7 @@
},
{
"cell_type": "markdown",
- "id": "bf66ad96",
+ "id": "35f57f40",
"metadata": {},
"source": [
"
-
@@ -807,42 +807,42 @@
<pandas.core.resample.DatetimeIndexResampler object at 0x107bf6b40>
+<pandas.core.resample.DatetimeIndexResampler object at 0x10f1fe6f0>
resample()
2019-01-01
20.0
- 5.745064
+ 5.787015
2019-04-01
50.0
- 5.859548
+ 5.446669
2019-07-01
80.0
- 5.203775
+ 4.783584
2019-10-01
110.0
- 5.682049
+ 4.189921
2020-01-01
20.0
- 4.721784
+ 4.630285
2020-04-01
50.0
- 4.513606
+ 4.827361
2020-07-01
80.0
- 5.744879
+ 5.085162
2020-10-01
110.0
- 4.139697
+ 5.273773
@@ -883,12 +883,12 @@ resample()
2019-01-01
65.0
- 5.622609
+ 5.051797
2020-01-01
65.0
- 4.779991
+ 4.954145
@@ -973,12 +973,12 @@ resample()
2019-01-01
0.5547
- 0.154317
+ 0.201180
2020-01-01
0.5547
- 0.237913
+ 0.143355
@@ -1638,7 +1638,7 @@ 変化率の計算
-<pandas.core.groupby.generic.DataFrameGroupBy object at 0x1136ebfe0>
+<pandas.core.groupby.generic.DataFrameGroupBy object at 0x1181ab740>
@@ -1653,7 +1653,7 @@ 変化率の計算
-<pandas.core.groupby.generic.SeriesGroupBy object at 0x113cbbd70>
+<pandas.core.groupby.generic.SeriesGroupBy object at 0x1181cd280>
diff --git a/13a_Random_Variables.html b/13a_Random_Variables.html
index af71e3cd..8cefe07a 100644
--- a/13a_Random_Variables.html
+++ b/13a_Random_Variables.html
@@ -659,53 +659,53 @@ .cov
0
- 9.226527
- 59.884129
+ 9.986898
+ 65.226378
1
- 8.447087
- 10.864864
+ 10.950868
+ 25.126103
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- 9.089684
- 98.844441
+ 8.616695
+ 91.922990
3
- 9.307079
- 30.984169
+ 9.438771
+ 2.279898
4
- 10.704744
- 79.099151
+ 10.677754
+ 19.288365
5
- 9.598606
- 55.097851
+ 10.055099
+ 23.828399
6
- 9.372898
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+ 9.469716
+ 89.078437
7
- 8.954774
- 73.010548
+ 9.359286
+ 24.031391
8
- 10.789657
- 65.658884
+ 9.010822
+ 31.161343
9
- 9.109282
- 35.203200
+ 11.323700
+ 29.797652
@@ -746,13 +746,13 @@ .cov
X
- 0.551495
- 8.565577
+ 0.766032
+ -11.157834
Y
- 8.565577
- 882.945539
+ -11.157834
+ 945.832728
@@ -795,11 +795,11 @@ .cov
X
1.000000
- 0.388167
+ -0.414524
Y
- 0.388167
+ -0.414524
1.000000
@@ -816,7 +816,7 @@ .cov
-0.38816740703052205
+-0.4145235186574958
@@ -1019,53 +1019,53 @@ .cov()
0
- 10.743490
+ 8.268658
NaN
1
- 11.515666
- 10.743490
+ 9.506594
+ 8.268658
2
- 11.058309
- 11.515666
+ 10.519143
+ 9.506594
3
- 9.699965
- 11.058309
+ 10.633746
+ 10.519143
4
- 10.317081
- 9.699965
+ 10.210946
+ 10.633746
5
- 8.613991
- 10.317081
+ 11.047005
+ 10.210946
6
- 11.934332
- 8.613991
+ 10.337397
+ 11.047005
7
- 11.172057
- 11.934332
+ 11.335130
+ 10.337397
8
- 10.105710
- 11.172057
+ 8.454739
+ 11.335130
9
- 10.341831
- 10.105710
+ 9.659399
+ 8.454739
@@ -1114,13 +1114,13 @@ .cov()
X
- 0.921925
- -0.137977
+ 1.050337
+ 0.061156
X_lag
- -0.137977
- 1.031133
+ 0.061156
+ 1.165773
@@ -1165,11 +1165,11 @@ .cov()
X
1.000000
- -0.133756
+ 0.064691
X_lag
- -0.133756
+ 0.064691
1.000000
@@ -1186,7 +1186,7 @@ .cov()
--0.133756232065724
+0.06469054006502663
@@ -1203,7 +1203,7 @@ .cov()
--0.133756232065724
+0.06469054006502663
@@ -1277,8 +1277,8 @@ 平均と分散
-array([5.99572137, 6.01985899, 4.28637238, 4.18736439, 5.03320963,
- 8.3873237 , 7.7770293 , 8.10349139, 7.5331098 , 4.70405868])
+array([3.99688835, 7.35944867, 4.80803364, 9.79589432, 5.00834094,
+ 5.32001356, 5.13081879, 3.75959095, 5.22039544, 5.39445347])
@@ -1302,7 +1302,7 @@ 平均と分散
-
+
２つの特徴がある。
@@ -1318,7 +1318,7 @@ 平均と分散
-(0.04193280260752992, 0.9610707122130532)
+(0.13031856002176803, 1.0106524139014506)
@@ -1333,7 +1333,7 @@ 平均と分散
-
+
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。
@@ -1374,28 +1374,28 @@ 自己共分散
-
+
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。
@@ -1431,7 +1431,7 @@ 自己共分散
-
+
resample()
2019-01-01
65.0
- 5.622609
+ 5.051797
2020-01-01
65.0
- 4.779991
+ 4.954145
@@ -973,12 +973,12 @@ resample()
2019-01-01
0.5547
- 0.154317
+ 0.201180
2020-01-01
0.5547
- 0.237913
+ 0.143355
@@ -1638,7 +1638,7 @@ 変化率の計算
-<pandas.core.groupby.generic.DataFrameGroupBy object at 0x1136ebfe0>
+<pandas.core.groupby.generic.DataFrameGroupBy object at 0x1181ab740>
@@ -1653,7 +1653,7 @@ 変化率の計算
-<pandas.core.groupby.generic.SeriesGroupBy object at 0x113cbbd70>
+<pandas.core.groupby.generic.SeriesGroupBy object at 0x1181cd280>
diff --git a/13a_Random_Variables.html b/13a_Random_Variables.html
index af71e3cd..8cefe07a 100644
--- a/13a_Random_Variables.html
+++ b/13a_Random_Variables.html
@@ -659,53 +659,53 @@ .cov
0
- 9.226527
- 59.884129
+ 9.986898
+ 65.226378
1
- 8.447087
- 10.864864
+ 10.950868
+ 25.126103
2
- 9.089684
- 98.844441
+ 8.616695
+ 91.922990
3
- 9.307079
- 30.984169
+ 9.438771
+ 2.279898
4
- 10.704744
- 79.099151
+ 10.677754
+ 19.288365
5
- 9.598606
- 55.097851
+ 10.055099
+ 23.828399
6
- 9.372898
- 8.376976
+ 9.469716
+ 89.078437
7
- 8.954774
- 73.010548
+ 9.359286
+ 24.031391
8
- 10.789657
- 65.658884
+ 9.010822
+ 31.161343
9
- 9.109282
- 35.203200
+ 11.323700
+ 29.797652
@@ -746,13 +746,13 @@ .cov
X
- 0.551495
- 8.565577
+ 0.766032
+ -11.157834
Y
- 8.565577
- 882.945539
+ -11.157834
+ 945.832728
@@ -795,11 +795,11 @@ .cov
X
1.000000
- 0.388167
+ -0.414524
Y
- 0.388167
+ -0.414524
1.000000
@@ -816,7 +816,7 @@ .cov
-0.38816740703052205
+-0.4145235186574958
@@ -1019,53 +1019,53 @@ .cov()
0
- 10.743490
+ 8.268658
NaN
1
- 11.515666
- 10.743490
+ 9.506594
+ 8.268658
2
- 11.058309
- 11.515666
+ 10.519143
+ 9.506594
3
- 9.699965
- 11.058309
+ 10.633746
+ 10.519143
4
- 10.317081
- 9.699965
+ 10.210946
+ 10.633746
5
- 8.613991
- 10.317081
+ 11.047005
+ 10.210946
6
- 11.934332
- 8.613991
+ 10.337397
+ 11.047005
7
- 11.172057
- 11.934332
+ 11.335130
+ 10.337397
8
- 10.105710
- 11.172057
+ 8.454739
+ 11.335130
9
- 10.341831
- 10.105710
+ 9.659399
+ 8.454739
@@ -1114,13 +1114,13 @@ .cov()
X
- 0.921925
- -0.137977
+ 1.050337
+ 0.061156
X_lag
- -0.137977
- 1.031133
+ 0.061156
+ 1.165773
@@ -1165,11 +1165,11 @@ .cov()
X
1.000000
- -0.133756
+ 0.064691
X_lag
- -0.133756
+ 0.064691
1.000000
@@ -1186,7 +1186,7 @@ .cov()
--0.133756232065724
+0.06469054006502663
@@ -1203,7 +1203,7 @@ .cov()
--0.133756232065724
+0.06469054006502663
@@ -1277,8 +1277,8 @@ 平均と分散
-array([5.99572137, 6.01985899, 4.28637238, 4.18736439, 5.03320963,
- 8.3873237 , 7.7770293 , 8.10349139, 7.5331098 , 4.70405868])
+array([3.99688835, 7.35944867, 4.80803364, 9.79589432, 5.00834094,
+ 5.32001356, 5.13081879, 3.75959095, 5.22039544, 5.39445347])
@@ -1302,7 +1302,7 @@ 平均と分散
-
+
２つの特徴がある。
@@ -1318,7 +1318,7 @@ 平均と分散
-(0.04193280260752992, 0.9610707122130532)
+(0.13031856002176803, 1.0106524139014506)
@@ -1333,7 +1333,7 @@ 平均と分散
-
+
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。
@@ -1374,28 +1374,28 @@ 自己共分散
-
+
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。
@@ -1431,7 +1431,7 @@ 自己共分散
-
+
resample()
2019-01-01
0.5547
- 0.154317
+ 0.201180
2020-01-01
0.5547
- 0.237913
+ 0.143355
@@ -1638,7 +1638,7 @@ 変化率の計算
-<pandas.core.groupby.generic.DataFrameGroupBy object at 0x1136ebfe0>
+<pandas.core.groupby.generic.DataFrameGroupBy object at 0x1181ab740>
@@ -1653,7 +1653,7 @@ 変化率の計算
-<pandas.core.groupby.generic.SeriesGroupBy object at 0x113cbbd70>
+<pandas.core.groupby.generic.SeriesGroupBy object at 0x1181cd280>
diff --git a/13a_Random_Variables.html b/13a_Random_Variables.html
index af71e3cd..8cefe07a 100644
--- a/13a_Random_Variables.html
+++ b/13a_Random_Variables.html
@@ -659,53 +659,53 @@ .cov
0
- 9.226527
- 59.884129
+ 9.986898
+ 65.226378
1
- 8.447087
- 10.864864
+ 10.950868
+ 25.126103
2
- 9.089684
- 98.844441
+ 8.616695
+ 91.922990
3
- 9.307079
- 30.984169
+ 9.438771
+ 2.279898
4
- 10.704744
- 79.099151
+ 10.677754
+ 19.288365
5
- 9.598606
- 55.097851
+ 10.055099
+ 23.828399
6
- 9.372898
- 8.376976
+ 9.469716
+ 89.078437
7
- 8.954774
- 73.010548
+ 9.359286
+ 24.031391
8
- 10.789657
- 65.658884
+ 9.010822
+ 31.161343
9
- 9.109282
- 35.203200
+ 11.323700
+ 29.797652
@@ -746,13 +746,13 @@ .cov
X
- 0.551495
- 8.565577
+ 0.766032
+ -11.157834
Y
- 8.565577
- 882.945539
+ -11.157834
+ 945.832728
@@ -795,11 +795,11 @@ .cov
X
1.000000
- 0.388167
+ -0.414524
Y
- 0.388167
+ -0.414524
1.000000
@@ -816,7 +816,7 @@ .cov
-0.38816740703052205
+-0.4145235186574958
@@ -1019,53 +1019,53 @@ .cov()
0
- 10.743490
+ 8.268658
NaN
1
- 11.515666
- 10.743490
+ 9.506594
+ 8.268658
2
- 11.058309
- 11.515666
+ 10.519143
+ 9.506594
3
- 9.699965
- 11.058309
+ 10.633746
+ 10.519143
4
- 10.317081
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+ 10.633746
5
- 8.613991
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6
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7
- 11.172057
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+ 10.337397
8
- 10.105710
- 11.172057
+ 8.454739
+ 11.335130
9
- 10.341831
- 10.105710
+ 9.659399
+ 8.454739
@@ -1114,13 +1114,13 @@ .cov()
X
- 0.921925
- -0.137977
+ 1.050337
+ 0.061156
X_lag
- -0.137977
- 1.031133
+ 0.061156
+ 1.165773
@@ -1165,11 +1165,11 @@ .cov()
X
1.000000
- -0.133756
+ 0.064691
X_lag
- -0.133756
+ 0.064691
1.000000
@@ -1186,7 +1186,7 @@ .cov()
--0.133756232065724
+0.06469054006502663
@@ -1203,7 +1203,7 @@ .cov()
--0.133756232065724
+0.06469054006502663
@@ -1277,8 +1277,8 @@ 平均と分散
-array([5.99572137, 6.01985899, 4.28637238, 4.18736439, 5.03320963,
- 8.3873237 , 7.7770293 , 8.10349139, 7.5331098 , 4.70405868])
+array([3.99688835, 7.35944867, 4.80803364, 9.79589432, 5.00834094,
+ 5.32001356, 5.13081879, 3.75959095, 5.22039544, 5.39445347])
@@ -1302,7 +1302,7 @@ 平均と分散
-
+
２つの特徴がある。
@@ -1318,7 +1318,7 @@ 平均と分散
-(0.04193280260752992, 0.9610707122130532)
+(0.13031856002176803, 1.0106524139014506)
@@ -1333,7 +1333,7 @@ 平均と分散
-
+
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。
@@ -1374,28 +1374,28 @@ 自己共分散
-
+
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。
@@ -1431,7 +1431,7 @@ 自己共分散
-
+
変化率の計算
-<pandas.core.groupby.generic.DataFrameGroupBy object at 0x1136ebfe0>
+<pandas.core.groupby.generic.DataFrameGroupBy object at 0x1181ab740>
@@ -1653,7 +1653,7 @@ 変化率の計算
-<pandas.core.groupby.generic.SeriesGroupBy object at 0x113cbbd70>
+<pandas.core.groupby.generic.SeriesGroupBy object at 0x1181cd280>
diff --git a/13a_Random_Variables.html b/13a_Random_Variables.html
index af71e3cd..8cefe07a 100644
--- a/13a_Random_Variables.html
+++ b/13a_Random_Variables.html
@@ -659,53 +659,53 @@ .cov
0
- 9.226527
- 59.884129
+ 9.986898
+ 65.226378
1
- 8.447087
- 10.864864
+ 10.950868
+ 25.126103
2
- 9.089684
- 98.844441
+ 8.616695
+ 91.922990
3
- 9.307079
- 30.984169
+ 9.438771
+ 2.279898
4
- 10.704744
- 79.099151
+ 10.677754
+ 19.288365
5
- 9.598606
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+ 23.828399
6
- 9.372898
- 8.376976
+ 9.469716
+ 89.078437
7
- 8.954774
- 73.010548
+ 9.359286
+ 24.031391
8
- 10.789657
- 65.658884
+ 9.010822
+ 31.161343
9
- 9.109282
- 35.203200
+ 11.323700
+ 29.797652
@@ -746,13 +746,13 @@ .cov
X
- 0.551495
- 8.565577
+ 0.766032
+ -11.157834
Y
- 8.565577
- 882.945539
+ -11.157834
+ 945.832728
@@ -795,11 +795,11 @@ .cov
X
1.000000
- 0.388167
+ -0.414524
Y
- 0.388167
+ -0.414524
1.000000
@@ -816,7 +816,7 @@ .cov
-0.38816740703052205
+-0.4145235186574958
@@ -1019,53 +1019,53 @@ .cov()
0
- 10.743490
+ 8.268658
NaN
1
- 11.515666
- 10.743490
+ 9.506594
+ 8.268658
2
- 11.058309
- 11.515666
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+ 9.506594
3
- 9.699965
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4
- 10.317081
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5
- 8.613991
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+ 10.210946
6
- 11.934332
- 8.613991
+ 10.337397
+ 11.047005
7
- 11.172057
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8
- 10.105710
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+ 8.454739
+ 11.335130
9
- 10.341831
- 10.105710
+ 9.659399
+ 8.454739
@@ -1114,13 +1114,13 @@ .cov()
X
- 0.921925
- -0.137977
+ 1.050337
+ 0.061156
X_lag
- -0.137977
- 1.031133
+ 0.061156
+ 1.165773
@@ -1165,11 +1165,11 @@ .cov()
X
1.000000
- -0.133756
+ 0.064691
X_lag
- -0.133756
+ 0.064691
1.000000
@@ -1186,7 +1186,7 @@ .cov()
--0.133756232065724
+0.06469054006502663
@@ -1203,7 +1203,7 @@ .cov()
--0.133756232065724
+0.06469054006502663
@@ -1277,8 +1277,8 @@ 平均と分散
-array([5.99572137, 6.01985899, 4.28637238, 4.18736439, 5.03320963,
- 8.3873237 , 7.7770293 , 8.10349139, 7.5331098 , 4.70405868])
+array([3.99688835, 7.35944867, 4.80803364, 9.79589432, 5.00834094,
+ 5.32001356, 5.13081879, 3.75959095, 5.22039544, 5.39445347])
@@ -1302,7 +1302,7 @@ 平均と分散
-
+
２つの特徴がある。
@@ -1318,7 +1318,7 @@ 平均と分散
-(0.04193280260752992, 0.9610707122130532)
+(0.13031856002176803, 1.0106524139014506)
@@ -1333,7 +1333,7 @@ 平均と分散
-
+
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。
@@ -1374,28 +1374,28 @@ 自己共分散
-
+
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。
@@ -1431,7 +1431,7 @@ 自己共分散
-
+
<pandas.core.groupby.generic.DataFrameGroupBy object at 0x1136ebfe0>
+<pandas.core.groupby.generic.DataFrameGroupBy object at 0x1181ab740>
変化率の計算
-<pandas.core.groupby.generic.SeriesGroupBy object at 0x113cbbd70>
+<pandas.core.groupby.generic.SeriesGroupBy object at 0x1181cd280>
diff --git a/13a_Random_Variables.html b/13a_Random_Variables.html
index af71e3cd..8cefe07a 100644
--- a/13a_Random_Variables.html
+++ b/13a_Random_Variables.html
@@ -659,53 +659,53 @@ .cov
0
- 9.226527
- 59.884129
+ 9.986898
+ 65.226378
1
- 8.447087
- 10.864864
+ 10.950868
+ 25.126103
2
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4
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5
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6
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7
- 8.954774
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8
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+ 9.010822
+ 31.161343
9
- 9.109282
- 35.203200
+ 11.323700
+ 29.797652
@@ -746,13 +746,13 @@ .cov
X
- 0.551495
- 8.565577
+ 0.766032
+ -11.157834
Y
- 8.565577
- 882.945539
+ -11.157834
+ 945.832728
@@ -795,11 +795,11 @@ .cov
X
1.000000
- 0.388167
+ -0.414524
Y
- 0.388167
+ -0.414524
1.000000
@@ -816,7 +816,7 @@ .cov
-0.38816740703052205
+-0.4145235186574958
@@ -1019,53 +1019,53 @@ .cov()
0
- 10.743490
+ 8.268658
NaN
1
- 11.515666
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+ 8.268658
2
- 11.058309
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3
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5
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6
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7
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8
- 10.105710
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+ 8.454739
+ 11.335130
9
- 10.341831
- 10.105710
+ 9.659399
+ 8.454739
@@ -1114,13 +1114,13 @@ .cov()
X
- 0.921925
- -0.137977
+ 1.050337
+ 0.061156
X_lag
- -0.137977
- 1.031133
+ 0.061156
+ 1.165773
@@ -1165,11 +1165,11 @@ .cov()
X
1.000000
- -0.133756
+ 0.064691
X_lag
- -0.133756
+ 0.064691
1.000000
@@ -1186,7 +1186,7 @@ .cov()
--0.133756232065724
+0.06469054006502663
@@ -1203,7 +1203,7 @@ .cov()
--0.133756232065724
+0.06469054006502663
@@ -1277,8 +1277,8 @@ 平均と分散
-array([5.99572137, 6.01985899, 4.28637238, 4.18736439, 5.03320963,
- 8.3873237 , 7.7770293 , 8.10349139, 7.5331098 , 4.70405868])
+array([3.99688835, 7.35944867, 4.80803364, 9.79589432, 5.00834094,
+ 5.32001356, 5.13081879, 3.75959095, 5.22039544, 5.39445347])
@@ -1302,7 +1302,7 @@ 平均と分散
-
+
２つの特徴がある。
@@ -1318,7 +1318,7 @@ 平均と分散
-(0.04193280260752992, 0.9610707122130532)
+(0.13031856002176803, 1.0106524139014506)
@@ -1333,7 +1333,7 @@ 平均と分散
-
+
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。
@@ -1374,28 +1374,28 @@ 自己共分散
-
+
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。
@@ -1431,7 +1431,7 @@ 自己共分散
-
+
<pandas.core.groupby.generic.SeriesGroupBy object at 0x113cbbd70>
+<pandas.core.groupby.generic.SeriesGroupBy object at 0x1181cd280>
.cov
0
- 9.226527
- 59.884129
+ 9.986898
+ 65.226378
1
- 8.447087
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- 9.089684
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- 9.307079
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4
- 10.704744
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- 9.598606
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- 8.954774
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+ 9.010822
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9
- 9.109282
- 35.203200
+ 11.323700
+ 29.797652
@@ -746,13 +746,13 @@ .cov
X
- 0.551495
- 8.565577
+ 0.766032
+ -11.157834
Y
- 8.565577
- 882.945539
+ -11.157834
+ 945.832728
@@ -795,11 +795,11 @@ .cov
X
1.000000
- 0.388167
+ -0.414524
Y
- 0.388167
+ -0.414524
1.000000
@@ -816,7 +816,7 @@ .cov
.cov
X
- 0.551495
- 8.565577
+ 0.766032
+ -11.157834
Y
- 8.565577
- 882.945539
+ -11.157834
+ 945.832728
@@ -795,11 +795,11 @@ .cov
X
1.000000
- 0.388167
+ -0.414524
Y
- 0.388167
+ -0.414524
1.000000
@@ -816,7 +816,7 @@ .cov
.cov
X
1.000000
- 0.388167
+ -0.414524
Y
- 0.388167
+ -0.414524
1.000000
@@ -816,7 +816,7 @@ .cov
.cov
0.38816740703052205
+-0.4145235186574958
.cov()
0
- 10.743490
+ 8.268658
NaN
1
- 11.515666
- 10.743490
+ 9.506594
+ 8.268658
2
- 11.058309
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+ 10.519143
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3
- 9.699965
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+ 10.633746
+ 10.519143
4
- 10.317081
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+ 10.633746
5
- 8.613991
- 10.317081
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+ 10.210946
6
- 11.934332
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7
- 11.172057
- 11.934332
+ 11.335130
+ 10.337397
8
- 10.105710
- 11.172057
+ 8.454739
+ 11.335130
9
- 10.341831
- 10.105710
+ 9.659399
+ 8.454739
@@ -1114,13 +1114,13 @@ .cov()
X
- 0.921925
- -0.137977
+ 1.050337
+ 0.061156
X_lag
- -0.137977
- 1.031133
+ 0.061156
+ 1.165773
@@ -1165,11 +1165,11 @@ .cov()
X
1.000000
- -0.133756
+ 0.064691
X_lag
- -0.133756
+ 0.064691
1.000000
@@ -1186,7 +1186,7 @@ .cov()
.cov()
X
- 0.921925
- -0.137977
+ 1.050337
+ 0.061156
X_lag
- -0.137977
- 1.031133
+ 0.061156
+ 1.165773
@@ -1165,11 +1165,11 @@ .cov()
X
1.000000
- -0.133756
+ 0.064691
X_lag
- -0.133756
+ 0.064691
1.000000
@@ -1186,7 +1186,7 @@ .cov()
.cov()
X
1.000000
- -0.133756
+ 0.064691
X_lag
- -0.133756
+ 0.064691
1.000000
@@ -1186,7 +1186,7 @@ .cov()
.cov()
-
@@ -1203,7 +1203,7 @@
自己共分散
-
-0.133756232065724
+0.06469054006502663
.cov()
-
@@ -1277,8 +1277,8 @@ 平均と分散
-
平均と分散
-
-0.133756232065724
+0.06469054006502663
平均と分散
-array([5.99572137, 6.01985899, 4.28637238, 4.18736439, 5.03320963,
- 8.3873237 , 7.7770293 , 8.10349139, 7.5331098 , 4.70405868])
+array([3.99688835, 7.35944867, 4.80803364, 9.79589432, 5.00834094,
+ 5.32001356, 5.13081879, 3.75959095, 5.22039544, 5.39445347])
@@ -1302,7 +1302,7 @@ 平均と分散
-
+
array([5.99572137, 6.01985899, 4.28637238, 4.18736439, 5.03320963,
- 8.3873237 , 7.7770293 , 8.10349139, 7.5331098 , 4.70405868])
+array([3.99688835, 7.35944867, 4.80803364, 9.79589432, 5.00834094,
+ 5.32001356, 5.13081879, 3.75959095, 5.22039544, 5.39445347])
平均と分散
-
+
２つの特徴がある。
@@ -1318,7 +1318,7 @@平均と分散
-(0.04193280260752992, 0.9610707122130532)
+(0.13031856002176803, 1.0106524139014506)
@@ -1333,7 +1333,7 @@ 平均と分散
-
+
(0.04193280260752992, 0.9610707122130532)
+(0.13031856002176803, 1.0106524139014506)
平均と分散
-
+
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。
自己共分散
-
+
+
-
@@ -1472,13 +1472,13 @@
自己共分散
-0.2570667340828474
+-0.005097087246679094
@@ -1556,7 +1556,7 @@ 自己相関係数
-0.25706673408284736
+-0.005097087246679093
@@ -1667,7 +1667,7 @@ ３つの例：持続性の違い
-
+
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。
@@ -1678,7 +1678,7 @@ ３つの例：持続性の違い
-
+
0.2570667340828474
+-0.005097087246679094
自己相関係数
-0.25706673408284736
+-0.005097087246679093
@@ -1667,7 +1667,7 @@ ３つの例：持続性の違い
-
+
0.25706673408284736
+-0.005097087246679093
３つの例：持続性の違い
-
+
+
\(\rho\)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。
@@ -1689,7 +1689,7 @@３つの例：持続性の違い
-
+
\(\rho\)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。
diff --git a/13b_Stochastic_Solow.html b/13b_Stochastic_Solow.html
index 6990f05b..595b372d 100644
--- a/13b_Stochastic_Solow.html
+++ b/13b_Stochastic_Solow.html
@@ -1094,10 +1094,10 @@ TFP#
-TFPの自己相関係数：0.663
+TFPの自己相関係数：0.535
-
+
シミュレーションを行う度に図と自己相関係数は異なることになる。
@@ -1612,95 +1612,95 @@ 実行#<
8.500577e+05
1.000000
0.366461
- 272210.617761
- 213095.442439
+ 2.722106e+05
+ 2.130954e+05
59115.175322
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8.879214e+05
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0.367346
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- 1.094660e+06
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0.369123
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4
- 1.272217e+06
- 1.718926
+ 1.402795e+06
+ 0.725768
0.370015
- 546252.979147
- 427624.834154
- 118628.144993
- 13.926802
- 12.946903
- 0.096481
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- 49.182744
- 12.474174
- 49.182744
- 11.191922
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+ 2.388969e+05
+ 1.870163e+05
+ 51880.526247
+ 14.003574
+ 15.040307
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+ -42.356623
+ 12.753208
+ -36.942112
+ 12.508372
+ -36.942112
+ 11.226120
+ -36.942112
@@ -1716,7 +1716,7 @@ 実行#<
-
+
トレンドの傾きは成長率を表しているが，徐々に減少していることが分かる。最初は成長率に対する資本蓄積の効果が大きいが，定常状態に近づくにつれて資本蓄積の効果が減少しているためである。
@@ -1730,7 +1730,7 @@ 実行#<
-
+
絶対値で概ね2％内に収まった変動となっている。データでは，リーマンショック時はマイナス約4％程乖離したが，それ以外は絶対値で2％以内に収まっており，シミュレーションは概ねデータと同じような特徴を持っていると言える。
@@ -1754,11 +1754,11 @@ 結果１：自己相関
--- シミュレーション：変動の自己相関係数 ---
-Yの変動： 0.395
-Cの変動： 0.395
-Iの変動： 0.395
-Kの変動： 0.828
-Aの変動： 0.394
+Yの変動： 0.538
+Cの変動： 0.538
+Iの変動： 0.538
+Kの変動： 0.901
+Aの変動： 0.532
@@ -1842,8 +1842,8 @@ 結果２：GDPとの相関\(h\)
の推定値
Model: OLS Adj. R-squared: 0.688
Method: Least Squares F-statistic: 384.1
Date: Fri, 03 Jan 2025 Prob (F-statistic): 8.56e-46
-Time: 01:09:49 Log-Likelihood: 716.66
+Time: 01:30:09 Log-Likelihood: 716.66
No. Observations: 175 AIC: -1429.
Df Residuals: 173 BIC: -1423.
Df Model: 1
@@ -1348,7 +1348,7 @@ TFPの自己相関係数：0.663
+TFPの自己相関係数：0.535
-
+
シミュレーションを行う度に図と自己相関係数は異なることになる。
@@ -1612,95 +1612,95 @@実行#<
8.500577e+05
1.000000
0.366461
- 272210.617761
- 213095.442439
+ 2.722106e+05
+ 2.130954e+05
59115.175322
- 13.704888
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- 0.083737
- -8.373726
- 12.616727
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- 12.371891
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+ 13.780344
+ -12.728463
+ 0.073138
+ -7.313825
+ 12.633292
+ -11.896071
+ 12.388456
+ -11.896071
+ 11.106204
+ -11.896071
1
8.879214e+05
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0.367346
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+ 1.445601e+05
+ 1.131664e+05
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+ 12.663656
+ -78.220508
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+ -78.220508
+ 11.136567
+ -78.220508
2
- 9.232819e+05
- 3.177727
+ 8.971171e+05
+ 7.485312
0.368233
- 895439.064586
- 700979.209461
- 194459.855125
- 13.816080
- -8.039004
- 0.090150
- 106.601600
- 12.667994
- 103.707559
- 12.423158
- 103.707559
- 11.140905
- 103.707559
+ 2.087540e+06
+ 1.634195e+06
+ 453344.817356
+ 13.892510
+ -18.556844
+ 0.088586
+ 192.435649
+ 12.693945
+ 185.755185
+ 12.449109
+ 185.755185
+ 11.166856
+ 185.755185
3
- 1.094660e+06
- 3.142032
+ 1.328034e+06
+ 1.544094
0.369123
- 943621.976175
- 738698.380549
- 204923.595627
- 13.871555
- 3.439931
- 0.093143
- 105.172659
- 12.693371
- 106.411034
- 12.448535
- 106.411034
- 11.166282
- 106.411034
+ 4.971370e+05
+ 3.891752e+05
+ 107961.777870
+ 13.948307
+ 15.090339
+ 0.095738
+ 33.869922
+ 12.723597
+ 39.302444
+ 12.478761
+ 39.302444
+ 11.196508
+ 39.302444
4
- 1.272217e+06
- 1.718926
+ 1.402795e+06
+ 0.725768
0.370015
- 546252.979147
- 427624.834154
- 118628.144993
- 13.926802
- 12.946903
- 0.096481
- 44.521859
- 12.719010
- 49.182744
- 12.474174
- 49.182744
- 11.191922
- 49.182744
+ 2.388969e+05
+ 1.870163e+05
+ 51880.526247
+ 14.003574
+ 15.040307
+ 0.103041
+ -42.356623
+ 12.753208
+ -36.942112
+ 12.508372
+ -36.942112
+ 11.226120
+ -36.942112
@@ -1716,7 +1716,7 @@ 実行#<
+
-
+
+
--- シミュレーション：変動の自己相関係数 ---
-Yの変動： 0.395
-Cの変動： 0.395
-Iの変動： 0.395
-Kの変動： 0.828
-Aの変動： 0.394
+Yの変動： 0.538
+Cの変動： 0.538
+Iの変動： 0.538
+Kの変動： 0.901
+Aの変動： 0.532
結果２：GDPとの相関\(h\)
最初のスイッチ：\(c\)残差の自己相関の検定
-\(H_0\)：残差は独立分布（無相関）
\(H_A\)：\(\rho_{p}\ne0\)
\(H_0\)：残差は独立分布
\(H_A\)：残差は独立分布ではない
\(u_t\)と\(v_t\)が毎期毎期変動しており，その結果として\(p_t\)と\(y_t\)が変動していることになる。
@@ -1095,7 +1095,7 @@
プロット
-
+
このプロットから次の点を確認できる。
@@ -1149,8 +1149,8 @@ GDPと価格水準の乖離率の標準偏差
-yの標準偏差:0.01375
-pの標準偏差:0.01415
+yの標準偏差:0.01379
+pの標準偏差:0.01421
@@ -1200,8 +1200,8 @@ 自己相関係数
-y:0.043
-p:0.819
+y:0.049
+p:0.821
@@ -1247,7 +1247,7 @@ p
--0.10826051696903893
+-0.11107441089736105
@@ -1278,11 +1278,11 @@ 結果のまとめと拡張-0.15298
WNショック
0.01375
0.01415
0.04270
0.81852
-0.10826
0.01379
0.01421
0.04869
0.82093
-0.11107
AR(1)ショック
0.01252
\(p_t\)に対する影響
需要ショックと供給ショックに起因する\(p_t\)の変動の割合を計算するために，式(144)の両辺を\(\text{Var}(p_{t})\)で割ると次式となる。
-
-(145)#\[\begin{align}
+
+(145)#\[\begin{align}
1&=
\frac{(ah)^2}{1-h^2}\cdot\frac{\text{Var}(u_{t})}{\text{Var}(p_{t})}
+\frac{h^2}{1-h^2}\cdot\frac{\text{Var}(v_{t})}{\text{Var}(p_{t})}
@@ -1580,8 +1580,8 @@ \(y_t\)に対する影響
\(p_t\)の総変動の大きさ（水準）を決定する上で，\(h\) が重要な役割を果たしている。\(h\)はは約0.8であり\(p_t\)の高い持続性を意味する。持続性が高い場合，一旦総供給曲線が定常状態の位置から離れると元の位置に戻るには時間が掛かることになる。即ち，定常状態から離れた状態が長くなる。そのような状況下で，更にショックが発生すると，定常状態から更に乖離する結果につながることになり，変動が増幅されることになる。その効果が\(\dfrac{h^2}{1-h^2}\)で捉えられている。
需要ショックと供給ショックに起因する\(y_t\)の変動の割合を計算するために，式(150)の両辺を\(\text{Var}(y_{t})\)で割ると次式となる。
-
-(151)#\[\begin{align}
+
+(151)#\[\begin{align}
1
&=\frac{h^2}{1-h^2}2ach\frac{\text{Var}(u_{t})}{\text{Var}(y_{t})}
+\frac{h^2}{1-h^2}c^2\frac{\text{Var}(v_{t})}{\text{Var}(y_{t})}\\
@@ -1814,8 +1814,8 @@ 付録#<
付録Ｂ：式(150)の導出#
-
-(152)#\[\begin{align}
+
+(152)#\[\begin{align}
\text{Var}(y_{t})
&=(ch)^2\text{Var}(p_{t})+\text{Var}(e_{yt})\\
&=(ch)^2\left[
@@ -1839,8 +1839,8 @@ 付録#<
+\frac{(ch)^2}{1-h^2}\text{Var}(v_{t})
\end{align}\]
ここで
-
-(153)#\[\begin{align}
+
+(153)#\[\begin{align}
1+(ach)^2-h^2
&=1+h^2[(ac)^2-1]=1+\frac{(ac)^2-1}{(1+ac)^2}\\
&=1+\frac{(ac+1)(ac-1)}{(1+ac)^2}=1+\frac{ac-1}{1+ac}\\
@@ -1852,8 +1852,8 @@ 付録#<
付録Ｃ：式(u-y)と(v-y)の導出#
式(u-y)に式(150)を代入して整理する。
-
-(154)#\[\begin{align}
+
+(154)#\[\begin{align}
\left[
\begin{split}
&y_t\text{の変動に対する}\\
@@ -1880,8 +1880,8 @@ 付録#<
\tag{u-y}
\end{align}\]
同様に式(v-y)に式(150)を代入して整理する。
-
-(155)#\[\begin{align}
+
+(155)#\[\begin{align}
\left[
\begin{split}
&p_t\text{の変動に対する}\\
diff --git a/6_Regression.html b/6_Regression.html
index bf5f3ada..9b05fb5c 100644
--- a/6_Regression.html
+++ b/6_Regression.html
@@ -611,7 +611,7 @@ 回帰分析#
Model: OLS Adj. R-squared: 0.848
Method: Least Squares F-statistic: 336.7
Date: Fri, 03 Jan 2025 Prob (F-statistic): 4.64e-26
-Time: 01:10:19 Log-Likelihood: 49.767
+Time: 01:30:30 Log-Likelihood: 49.767
No. Observations: 61 AIC: -95.53
Df Residuals: 59 BIC: -91.31
Df Model: 1
diff --git a/_images/0024ddef8095e4097129da990898d8b196ffe7fcac4cd02882096ce75003f2cd.png b/_images/0024ddef8095e4097129da990898d8b196ffe7fcac4cd02882096ce75003f2cd.png
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index 00000000..840d6a00
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deleted file mode 100644
index e48e7669..00000000
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diff --git a/_images/f9e9b83dd3a04363211d9757cffe47aeb643db32d911a7fb1feaf926ad9a087a.png b/_images/f9e9b83dd3a04363211d9757cffe47aeb643db32d911a7fb1feaf926ad9a087a.png
new file mode 100644
index 00000000..ba24f8c4
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diff --git a/_sources/18_ADAS-1.ipynb b/_sources/18_ADAS-1.ipynb
index 768981cf..cb024c4b 100644
--- a/_sources/18_ADAS-1.ipynb
+++ b/_sources/18_ADAS-1.ipynb
@@ -1629,8 +1629,8 @@
"\n",
"＜帰無仮説＞\n",
"\n",
- "* $H_0$：残差は独立分布（無相関）\n",
- "* $H_A$：$\\rho_{p}\\ne0$"
+ "* $H_0$：残差は独立分布\n",
+ "* $H_A$：残差は独立分布ではない"
]
},
{
@@ -1799,7 +1799,9 @@
},
{
"cell_type": "markdown",
- "metadata": {},
+ "metadata": {
+ "jp-MarkdownHeadingCollapsed": true
+ },
"source": [
"(sec:18-1-appendix_B)=\n",
"### 付録Ｂ"
diff --git a/_sources/index.ipynb b/_sources/index.ipynb
index 37b33d95..bca03462 100644
--- a/_sources/index.ipynb
+++ b/_sources/index.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "9515b5c2",
+ "id": "fb39b6c9",
"metadata": {},
"source": [
"# Pythonで学ぶマクロ経済学 (中級＋レベル)\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": 1,
- "id": "f0488bae",
+ "id": "aab734a9",
"metadata": {},
"outputs": [
{
@@ -41,7 +41,7 @@
},
{
"cell_type": "markdown",
- "id": "bf66ad96",
+ "id": "35f57f40",
"metadata": {},
"source": [
"
\(H_0\)：残差は独立分布（無相関）
\(H_A\)：\(\rho_{p}\ne0\)
\(H_0\)：残差は独立分布
\(H_A\)：残差は独立分布ではない
+
-
+
+
このプロットから次の点を確認できる。
@@ -1149,8 +1149,8 @@GDPと価格水準の乖離率の標準偏差
-yの標準偏差:0.01375
-pの標準偏差:0.01415
+yの標準偏差:0.01379
+pの標準偏差:0.01421
@@ -1200,8 +1200,8 @@ 自己相関係数
-y:0.043
-p:0.819
+y:0.049
+p:0.821
@@ -1247,7 +1247,7 @@ p
--0.10826051696903893
+-0.11107441089736105
@@ -1278,11 +1278,11 @@ 結果のまとめと拡張-0.15298
WNショック
0.01375
0.01415
0.04270
0.81852
-0.10826
0.01379
0.01421
0.04869
0.82093
-0.11107
AR(1)ショック
0.01252
\(p_t\)に対する影響
需要ショックと供給ショックに起因する\(p_t\)の変動の割合を計算するために，式(144)の両辺を\(\text{Var}(p_{t})\)で割ると次式となる。
-
-(145)#\[\begin{align}
+
+(145)#\[\begin{align}
1&=
\frac{(ah)^2}{1-h^2}\cdot\frac{\text{Var}(u_{t})}{\text{Var}(p_{t})}
+\frac{h^2}{1-h^2}\cdot\frac{\text{Var}(v_{t})}{\text{Var}(p_{t})}
@@ -1580,8 +1580,8 @@ \(y_t\)に対する影響
\(p_t\)の総変動の大きさ（水準）を決定する上で，\(h\) が重要な役割を果たしている。\(h\)はは約0.8であり\(p_t\)の高い持続性を意味する。持続性が高い場合，一旦総供給曲線が定常状態の位置から離れると元の位置に戻るには時間が掛かることになる。即ち，定常状態から離れた状態が長くなる。そのような状況下で，更にショックが発生すると，定常状態から更に乖離する結果につながることになり，変動が増幅されることになる。その効果が\(\dfrac{h^2}{1-h^2}\)で捉えられている。
需要ショックと供給ショックに起因する\(y_t\)の変動の割合を計算するために，式(150)の両辺を\(\text{Var}(y_{t})\)で割ると次式となる。
-
-(151)#\[\begin{align}
+
+(151)#\[\begin{align}
1
&=\frac{h^2}{1-h^2}2ach\frac{\text{Var}(u_{t})}{\text{Var}(y_{t})}
+\frac{h^2}{1-h^2}c^2\frac{\text{Var}(v_{t})}{\text{Var}(y_{t})}\\
@@ -1814,8 +1814,8 @@ 付録#<
付録Ｂ：式(150)の導出#
-
-(152)#\[\begin{align}
+
+(152)#\[\begin{align}
\text{Var}(y_{t})
&=(ch)^2\text{Var}(p_{t})+\text{Var}(e_{yt})\\
&=(ch)^2\left[
@@ -1839,8 +1839,8 @@ 付録#<
+\frac{(ch)^2}{1-h^2}\text{Var}(v_{t})
\end{align}\]
ここで
-
-(153)#\[\begin{align}
+
+(153)#\[\begin{align}
1+(ach)^2-h^2
&=1+h^2[(ac)^2-1]=1+\frac{(ac)^2-1}{(1+ac)^2}\\
&=1+\frac{(ac+1)(ac-1)}{(1+ac)^2}=1+\frac{ac-1}{1+ac}\\
@@ -1852,8 +1852,8 @@ 付録#<
付録Ｃ：式(u-y)と(v-y)の導出#
式(u-y)に式(150)を代入して整理する。
-
-(154)#\[\begin{align}
+
+(154)#\[\begin{align}
\left[
\begin{split}
&y_t\text{の変動に対する}\\
@@ -1880,8 +1880,8 @@ 付録#<
\tag{u-y}
\end{align}\]
同様に式(v-y)に式(150)を代入して整理する。
-
-(155)#\[\begin{align}
+
+(155)#\[\begin{align}
\left[
\begin{split}
&p_t\text{の変動に対する}\\
diff --git a/6_Regression.html b/6_Regression.html
index bf5f3ada..9b05fb5c 100644
--- a/6_Regression.html
+++ b/6_Regression.html
@@ -611,7 +611,7 @@ 回帰分析#
Model: OLS Adj. R-squared: 0.848
Method: Least Squares F-statistic: 336.7
Date: Fri, 03 Jan 2025 Prob (F-statistic): 4.64e-26
-Time: 01:10:19 Log-Likelihood: 49.767
+Time: 01:30:30 Log-Likelihood: 49.767
No. Observations: 61 AIC: -95.53
Df Residuals: 59 BIC: -91.31
Df Model: 1
diff --git a/_images/0024ddef8095e4097129da990898d8b196ffe7fcac4cd02882096ce75003f2cd.png b/_images/0024ddef8095e4097129da990898d8b196ffe7fcac4cd02882096ce75003f2cd.png
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diff --git a/_sources/18_ADAS-1.ipynb b/_sources/18_ADAS-1.ipynb
index 768981cf..cb024c4b 100644
--- a/_sources/18_ADAS-1.ipynb
+++ b/_sources/18_ADAS-1.ipynb
@@ -1629,8 +1629,8 @@
"\n",
"＜帰無仮説＞\n",
"\n",
- "* $H_0$：残差は独立分布（無相関）\n",
- "* $H_A$：$\\rho_{p}\\ne0$"
+ "* $H_0$：残差は独立分布\n",
+ "* $H_A$：残差は独立分布ではない"
]
},
{
@@ -1799,7 +1799,9 @@
},
{
"cell_type": "markdown",
- "metadata": {},
+ "metadata": {
+ "jp-MarkdownHeadingCollapsed": true
+ },
"source": [
"(sec:18-1-appendix_B)=\n",
"### 付録Ｂ"
diff --git a/_sources/index.ipynb b/_sources/index.ipynb
index 37b33d95..bca03462 100644
--- a/_sources/index.ipynb
+++ b/_sources/index.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "9515b5c2",
+ "id": "fb39b6c9",
"metadata": {},
"source": [
"# Pythonで学ぶマクロ経済学 (中級＋レベル)\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": 1,
- "id": "f0488bae",
+ "id": "aab734a9",
"metadata": {},
"outputs": [
{
@@ -41,7 +41,7 @@
},
{
"cell_type": "markdown",
- "id": "bf66ad96",
+ "id": "35f57f40",
"metadata": {},
"source": [
"
yの標準偏差:0.01375
-pの標準偏差:0.01415
+yの標準偏差:0.01379
+pの標準偏差:0.01421
自己相関係数
-y:0.043
-p:0.819
+y:0.049
+p:0.821
@@ -1247,7 +1247,7 @@ p
y:0.043
-p:0.819
+y:0.049
+p:0.821
p
-0.10826051696903893
+-0.11107441089736105
結果のまとめと拡張-0.15298
WNショック
0.01375
0.01415
0.04270
0.81852
-0.10826
0.01379
0.01421
0.04869
0.82093
-0.11107
AR(1)ショック
0.01252
\(p_t\)に対する影響
需要ショックと供給ショックに起因する\(p_t\)の変動の割合を計算するために，式(144)の両辺を\(\text{Var}(p_{t})\)で割ると次式となる。
-
-(145)#\[\begin{align}
+
+(145)#\[\begin{align}
1&=
\frac{(ah)^2}{1-h^2}\cdot\frac{\text{Var}(u_{t})}{\text{Var}(p_{t})}
+\frac{h^2}{1-h^2}\cdot\frac{\text{Var}(v_{t})}{\text{Var}(p_{t})}
@@ -1580,8 +1580,8 @@ \(y_t\)に対する影響
\(p_t\)の総変動の大きさ（水準）を決定する上で，\(h\) が重要な役割を果たしている。\(h\)はは約0.8であり\(p_t\)の高い持続性を意味する。持続性が高い場合，一旦総供給曲線が定常状態の位置から離れると元の位置に戻るには時間が掛かることになる。即ち，定常状態から離れた状態が長くなる。そのような状況下で，更にショックが発生すると，定常状態から更に乖離する結果につながることになり，変動が増幅されることになる。その効果が\(\dfrac{h^2}{1-h^2}\)で捉えられている。
需要ショックと供給ショックに起因する\(y_t\)の変動の割合を計算するために，式(150)の両辺を\(\text{Var}(y_{t})\)で割ると次式となる。
-
-(151)#\[\begin{align}
+
+(151)#\[\begin{align}
1
&=\frac{h^2}{1-h^2}2ach\frac{\text{Var}(u_{t})}{\text{Var}(y_{t})}
+\frac{h^2}{1-h^2}c^2\frac{\text{Var}(v_{t})}{\text{Var}(y_{t})}\\
@@ -1814,8 +1814,8 @@ 付録#<
付録Ｂ：式(150)の導出#
-
-(152)#\[\begin{align}
+
+(152)#\[\begin{align}
\text{Var}(y_{t})
&=(ch)^2\text{Var}(p_{t})+\text{Var}(e_{yt})\\
&=(ch)^2\left[
@@ -1839,8 +1839,8 @@ 付録#<
+\frac{(ch)^2}{1-h^2}\text{Var}(v_{t})
\end{align}\]
ここで
-
-(153)#\[\begin{align}
+
+(153)#\[\begin{align}
1+(ach)^2-h^2
&=1+h^2[(ac)^2-1]=1+\frac{(ac)^2-1}{(1+ac)^2}\\
&=1+\frac{(ac+1)(ac-1)}{(1+ac)^2}=1+\frac{ac-1}{1+ac}\\
@@ -1852,8 +1852,8 @@ 付録#<
付録Ｃ：式(u-y)と(v-y)の導出#
式(u-y)に式(150)を代入して整理する。
-
-(154)#\[\begin{align}
+
+(154)#\[\begin{align}
\left[
\begin{split}
&y_t\text{の変動に対する}\\
@@ -1880,8 +1880,8 @@ 付録#<
\tag{u-y}
\end{align}\]
同様に式(v-y)に式(150)を代入して整理する。
-
-(155)#\[\begin{align}
+
+(155)#\[\begin{align}
\left[
\begin{split}
&p_t\text{の変動に対する}\\
diff --git a/6_Regression.html b/6_Regression.html
index bf5f3ada..9b05fb5c 100644
--- a/6_Regression.html
+++ b/6_Regression.html
@@ -611,7 +611,7 @@ 回帰分析#
Model: OLS Adj. R-squared: 0.848
Method: Least Squares F-statistic: 336.7
Date: Fri, 03 Jan 2025 Prob (F-statistic): 4.64e-26
-Time: 01:10:19 Log-Likelihood: 49.767
+Time: 01:30:30 Log-Likelihood: 49.767
No. Observations: 61 AIC: -95.53
Df Residuals: 59 BIC: -91.31
Df Model: 1
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deleted file mode 100644
index e48e7669..00000000
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diff --git a/_images/f9e9b83dd3a04363211d9757cffe47aeb643db32d911a7fb1feaf926ad9a087a.png b/_images/f9e9b83dd3a04363211d9757cffe47aeb643db32d911a7fb1feaf926ad9a087a.png
new file mode 100644
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diff --git a/_sources/18_ADAS-1.ipynb b/_sources/18_ADAS-1.ipynb
index 768981cf..cb024c4b 100644
--- a/_sources/18_ADAS-1.ipynb
+++ b/_sources/18_ADAS-1.ipynb
@@ -1629,8 +1629,8 @@
"\n",
"＜帰無仮説＞\n",
"\n",
- "* $H_0$：残差は独立分布（無相関）\n",
- "* $H_A$：$\\rho_{p}\\ne0$"
+ "* $H_0$：残差は独立分布\n",
+ "* $H_A$：残差は独立分布ではない"
]
},
{
@@ -1799,7 +1799,9 @@
},
{
"cell_type": "markdown",
- "metadata": {},
+ "metadata": {
+ "jp-MarkdownHeadingCollapsed": true
+ },
"source": [
"(sec:18-1-appendix_B)=\n",
"### 付録Ｂ"
diff --git a/_sources/index.ipynb b/_sources/index.ipynb
index 37b33d95..bca03462 100644
--- a/_sources/index.ipynb
+++ b/_sources/index.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "9515b5c2",
+ "id": "fb39b6c9",
"metadata": {},
"source": [
"# Pythonで学ぶマクロ経済学 (中級＋レベル)\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": 1,
- "id": "f0488bae",
+ "id": "aab734a9",
"metadata": {},
"outputs": [
{
@@ -41,7 +41,7 @@
},
{
"cell_type": "markdown",
- "id": "bf66ad96",
+ "id": "35f57f40",
"metadata": {},
"source": [
"
WNショック
0.01375
0.01415
0.04270
0.81852
-0.10826
0.01379
0.01421
0.04869
0.82093
-0.11107
AR(1)ショック
0.01252
\(p_t\)に対する影響
需要ショックと供給ショックに起因する\(p_t\)の変動の割合を計算するために，式(144)の両辺を\(\text{Var}(p_{t})\)で割ると次式となる。
-
-(145)#\[\begin{align}
+
+(145)#\[\begin{align}
1&=
\frac{(ah)^2}{1-h^2}\cdot\frac{\text{Var}(u_{t})}{\text{Var}(p_{t})}
+\frac{h^2}{1-h^2}\cdot\frac{\text{Var}(v_{t})}{\text{Var}(p_{t})}
@@ -1580,8 +1580,8 @@
\(y_t\)に対する影響
\(p_t\)の総変動の大きさ（水準）を決定する上で，\(h\) が重要な役割を果たしている。\(h\)はは約0.8であり\(p_t\)の高い持続性を意味する。持続性が高い場合，一旦総供給曲線が定常状態の位置から離れると元の位置に戻るには時間が掛かることになる。即ち，定常状態から離れた状態が長くなる。そのような状況下で，更にショックが発生すると，定常状態から更に乖離する結果につながることになり，変動が増幅されることになる。その効果が\(\dfrac{h^2}{1-h^2}\)で捉えられている。
需要ショックと供給ショックに起因する\(y_t\)の変動の割合を計算するために，式(150)の両辺を\(\text{Var}(y_{t})\)で割ると次式となる。
-
-(151)#\[\begin{align}
+
+(151)#\[\begin{align}
1
&=\frac{h^2}{1-h^2}2ach\frac{\text{Var}(u_{t})}{\text{Var}(y_{t})}
+\frac{h^2}{1-h^2}c^2\frac{\text{Var}(v_{t})}{\text{Var}(y_{t})}\\
@@ -1814,8 +1814,8 @@ 付録#<
付録#<
付録Ｂ：式(150)の導出#
-
-(152)#\[\begin{align}
+
+(152)#\[\begin{align}
\text{Var}(y_{t})
&=(ch)^2\text{Var}(p_{t})+\text{Var}(e_{yt})\\
&=(ch)^2\left[
@@ -1839,8 +1839,8 @@ 付録#<
+\frac{(ch)^2}{1-h^2}\text{Var}(v_{t})
\end{align}\]
ここで
-
-(153)#\[\begin{align}
+
+(153)#\[\begin{align}
1+(ach)^2-h^2
&=1+h^2[(ac)^2-1]=1+\frac{(ac)^2-1}{(1+ac)^2}\\
&=1+\frac{(ac+1)(ac-1)}{(1+ac)^2}=1+\frac{ac-1}{1+ac}\\
@@ -1852,8 +1852,8 @@ 付録#<
付録Ｃ：式(u-y)と(v-y)の導出#
式(u-y)に式(150)を代入して整理する。
-
-(154)#\[\begin{align}
+
+(154)#\[\begin{align}
\left[
\begin{split}
&y_t\text{の変動に対する}\\
@@ -1880,8 +1880,8 @@ 付録#<
\tag{u-y}
\end{align}\]
同様に式(v-y)に式(150)を代入して整理する。
-
-(155)#\[\begin{align}
+
+(155)#\[\begin{align}
\left[
\begin{split}
&p_t\text{の変動に対する}\\
diff --git a/6_Regression.html b/6_Regression.html
index bf5f3ada..9b05fb5c 100644
--- a/6_Regression.html
+++ b/6_Regression.html
@@ -611,7 +611,7 @@ 回帰分析#
Model: OLS Adj. R-squared: 0.848
Method: Least Squares F-statistic: 336.7
Date: Fri, 03 Jan 2025 Prob (F-statistic): 4.64e-26
-Time: 01:10:19 Log-Likelihood: 49.767
+Time: 01:30:30 Log-Likelihood: 49.767
No. Observations: 61 AIC: -95.53
Df Residuals: 59 BIC: -91.31
Df Model: 1
diff --git a/_images/0024ddef8095e4097129da990898d8b196ffe7fcac4cd02882096ce75003f2cd.png b/_images/0024ddef8095e4097129da990898d8b196ffe7fcac4cd02882096ce75003f2cd.png
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index 00000000..840d6a00
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deleted file mode 100644
index 44f51ede..00000000
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index a2c60668..00000000
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new file mode 100644
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index dbe7ab9f..00000000
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deleted file mode 100644
index e48e7669..00000000
Binary files a/_images/ebe1fd1db8278d9e821af856199b42a43efdd45dcd11760a2c34e82a46f786f9.png and /dev/null differ
diff --git a/_images/f9e9b83dd3a04363211d9757cffe47aeb643db32d911a7fb1feaf926ad9a087a.png b/_images/f9e9b83dd3a04363211d9757cffe47aeb643db32d911a7fb1feaf926ad9a087a.png
new file mode 100644
index 00000000..ba24f8c4
Binary files /dev/null and b/_images/f9e9b83dd3a04363211d9757cffe47aeb643db32d911a7fb1feaf926ad9a087a.png differ
diff --git a/_sources/18_ADAS-1.ipynb b/_sources/18_ADAS-1.ipynb
index 768981cf..cb024c4b 100644
--- a/_sources/18_ADAS-1.ipynb
+++ b/_sources/18_ADAS-1.ipynb
@@ -1629,8 +1629,8 @@
"\n",
"＜帰無仮説＞\n",
"\n",
- "* $H_0$：残差は独立分布（無相関）\n",
- "* $H_A$：$\\rho_{p}\\ne0$"
+ "* $H_0$：残差は独立分布\n",
+ "* $H_A$：残差は独立分布ではない"
]
},
{
@@ -1799,7 +1799,9 @@
},
{
"cell_type": "markdown",
- "metadata": {},
+ "metadata": {
+ "jp-MarkdownHeadingCollapsed": true
+ },
"source": [
"(sec:18-1-appendix_B)=\n",
"### 付録Ｂ"
diff --git a/_sources/index.ipynb b/_sources/index.ipynb
index 37b33d95..bca03462 100644
--- a/_sources/index.ipynb
+++ b/_sources/index.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "9515b5c2",
+ "id": "fb39b6c9",
"metadata": {},
"source": [
"# Pythonで学ぶマクロ経済学 (中級＋レベル)\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": 1,
- "id": "f0488bae",
+ "id": "aab734a9",
"metadata": {},
"outputs": [
{
@@ -41,7 +41,7 @@
},
{
"cell_type": "markdown",
- "id": "bf66ad96",
+ "id": "35f57f40",
"metadata": {},
"source": [
"
付録Ｂ：式(150)の導出#
-
-(152)#\[\begin{align}
+
+(152)#\[\begin{align}
\text{Var}(y_{t})
&=(ch)^2\text{Var}(p_{t})+\text{Var}(e_{yt})\\
&=(ch)^2\left[
@@ -1839,8 +1839,8 @@
付録#< +\frac{(ch)^2}{1-h^2}\text{Var}(v_{t}) \end{align}\]
ここで
-
-(153)#\[\begin{align}
+
+(153)#\[\begin{align}
1+(ach)^2-h^2
&=1+h^2[(ac)^2-1]=1+\frac{(ac)^2-1}{(1+ac)^2}\\
&=1+\frac{(ac+1)(ac-1)}{(1+ac)^2}=1+\frac{ac-1}{1+ac}\\
@@ -1852,8 +1852,8 @@ 付録#<
付録#<
付録Ｃ：式(u-y)と(v-y)の導出#
式(u-y)に式(150)を代入して整理する。
-
-(154)#\[\begin{align}
+
+(154)#\[\begin{align}
\left[
\begin{split}
&y_t\text{の変動に対する}\\
@@ -1880,8 +1880,8 @@ 付録#<
\tag{u-y}
\end{align}\]
同様に式(v-y)に式(150)を代入して整理する。
-
-(155)#\[\begin{align}
+
+(155)#\[\begin{align}
\left[
\begin{split}
&p_t\text{の変動に対する}\\
diff --git a/6_Regression.html b/6_Regression.html
index bf5f3ada..9b05fb5c 100644
--- a/6_Regression.html
+++ b/6_Regression.html
@@ -611,7 +611,7 @@ 回帰分析#
Model: OLS Adj. R-squared: 0.848
Method: Least Squares F-statistic: 336.7
Date: Fri, 03 Jan 2025 Prob (F-statistic): 4.64e-26
-Time: 01:10:19 Log-Likelihood: 49.767
+Time: 01:30:30 Log-Likelihood: 49.767
No. Observations: 61 AIC: -95.53
Df Residuals: 59 BIC: -91.31
Df Model: 1
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index e48e7669..00000000
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diff --git a/_images/f9e9b83dd3a04363211d9757cffe47aeb643db32d911a7fb1feaf926ad9a087a.png b/_images/f9e9b83dd3a04363211d9757cffe47aeb643db32d911a7fb1feaf926ad9a087a.png
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index 00000000..ba24f8c4
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diff --git a/_sources/18_ADAS-1.ipynb b/_sources/18_ADAS-1.ipynb
index 768981cf..cb024c4b 100644
--- a/_sources/18_ADAS-1.ipynb
+++ b/_sources/18_ADAS-1.ipynb
@@ -1629,8 +1629,8 @@
"\n",
"＜帰無仮説＞\n",
"\n",
- "* $H_0$：残差は独立分布（無相関）\n",
- "* $H_A$：$\\rho_{p}\\ne0$"
+ "* $H_0$：残差は独立分布\n",
+ "* $H_A$：残差は独立分布ではない"
]
},
{
@@ -1799,7 +1799,9 @@
},
{
"cell_type": "markdown",
- "metadata": {},
+ "metadata": {
+ "jp-MarkdownHeadingCollapsed": true
+ },
"source": [
"(sec:18-1-appendix_B)=\n",
"### 付録Ｂ"
diff --git a/_sources/index.ipynb b/_sources/index.ipynb
index 37b33d95..bca03462 100644
--- a/_sources/index.ipynb
+++ b/_sources/index.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "9515b5c2",
+ "id": "fb39b6c9",
"metadata": {},
"source": [
"# Pythonで学ぶマクロ経済学 (中級＋レベル)\n",
@@ -22,7 +22,7 @@
{
"cell_type": "code",
"execution_count": 1,
- "id": "f0488bae",
+ "id": "aab734a9",
"metadata": {},
"outputs": [
{
@@ -41,7 +41,7 @@
},
{
"cell_type": "markdown",
- "id": "bf66ad96",
+ "id": "35f57f40",
"metadata": {},
"source": [
"
付録Ｃ：式(u-y)と(v-y)の導出#
式(u-y)に式(150)を代入して整理する。
-
-(154)#\[\begin{align}
+
+(154)#\[\begin{align}
\left[
\begin{split}
&y_t\text{の変動に対する}\\
@@ -1880,8 +1880,8 @@
付録#< \tag{u-y} \end{align}\]
同様に式(v-y)に式(150)を代入して整理する。
-
-(155)#\[\begin{align}
+
+(155)#\[\begin{align}
\left[
\begin{split}
&p_t\text{の変動に対する}\\
diff --git a/6_Regression.html b/6_Regression.html
index bf5f3ada..9b05fb5c 100644
--- a/6_Regression.html
+++ b/6_Regression.html
@@ -611,7 +611,7 @@