GDPの場合#
+.covと.corr()と.autocorr()：GDPの場合#
まずGDPの変動を考えるために，dfからgdp_cycleをDataFrameとして抽出し，変数gに割り当てよう。
はっきりと正の相関を確認できるが，例外的な動きをしている観測値もある。
-GDPの構成要素#
+GDPの構成要素#
まずGDPの構成要素のトレンドからの乖離率の持続性を考察するが，gdp_cycleを含めて次の変数を考えよう。
@@ -2288,8 +2288,8 @@ GDPの構成要素
-
GDPの構成要素
-インフレ率と失業率#
+
+インフレ率と失業率#
次に、失業率とインフレ率の持続性を確認する。
各変数の乖離を計算するが、注意する点がある。GDPなどの変数と違い、インフレ率と失業率は長期的なトレンドはない。従って、式(101)を使い、対数化せずに計算する必要がる。
@@ -2337,8 +2337,8 @@ インフレ率と失業率
-変動の大きさ#
+
+変動の大きさ#
次に変動の大きさを考えるために，GDPの標準偏差に対するそれぞれの構成要素の標準偏差の比率を計算しよう。
diff --git a/11_Macro_Variables.html b/11_Macro_Variables.html
index 02c99fa4..1e422227 100644
--- a/11_Macro_Variables.html
+++ b/11_Macro_Variables.html
@@ -732,7 +732,7 @@ 回帰分析#
Model: OLS Adj. R-squared: 0.387
Method: Least Squares F-statistic: 111.5
Date: Sat, 17 Aug 2024 Prob (F-statistic): 1.84e-20
-Time: 01:23:12 Log-Likelihood: -275.03
+Time: 01:39:52 Log-Likelihood: -275.03
No. Observations: 176 AIC: 554.1
Df Residuals: 174 BIC: 560.4
Df Model: 1
@@ -1317,122 +1317,122 @@ resample()
2019-01-01
10
- 4.960362
+ 6.398947
2019-02-01
20
- 5.211487
+ 4.601473
2019-03-01
30
- 6.066279
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2019-04-01
40
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2019-05-01
50
- 6.421642
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2019-06-01
60
- 6.324687
+ 5.474436
2019-07-01
70
- 5.219173
+ 5.469829
2019-08-01
80
- 3.876284
+ 5.683622
2019-09-01
90
- 3.997646
+ 5.425678
2019-10-01
100
- 5.987195
+ 4.573360
2019-11-01
110
- 4.783851
+ 6.808362
2019-12-01
120
- 4.686246
+ 3.761755
2020-01-01
10
- 4.811122
+ 4.959200
2020-02-01
20
- 4.960091
+ 3.975104
2020-03-01
30
- 4.712852
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2020-04-01
40
- 4.745662
+ 5.606324
2020-05-01
50
- 5.217352
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2020-06-01
60
- 3.446441
+ 5.696802
2020-07-01
70
- 4.974370
+ 5.252175
2020-08-01
80
- 3.999436
+ 5.706897
2020-09-01
90
- 5.855918
+ 5.429330
2020-10-01
100
- 6.453502
+ 3.853960
2020-11-01
110
- 5.557520
+ 5.387163
2020-12-01
120
- 3.946524
+ 4.893141
@@ -1460,7 +1460,7 @@ resample()
-<pandas.core.resample.DatetimeIndexResampler object at 0x11cea8f80>
+<pandas.core.resample.DatetimeIndexResampler object at 0x110ee56d0>
@@ -1501,42 +1501,42 @@ resample()
2019-01-01
20.0
- 5.412709
+ 5.051900
2019-04-01
50.0
- 6.351174
+ 4.796580
2019-07-01
80.0
- 4.364368
+ 5.526376
2019-10-01
110.0
- 5.152431
+ 5.047826
2020-01-01
20.0
- 4.828021
+ 4.809558
2020-04-01
50.0
- 4.469819
+ 5.516914
2020-07-01
80.0
- 4.943241
+ 5.462801
2020-10-01
110.0
- 5.319182
+ 4.711421
@@ -1577,12 +1577,12 @@ resample()
2019-01-01
65.0
- 5.320170
+ 5.105670
2020-01-01
65.0
- 4.890066
+ 5.125174
@@ -1667,12 +1667,12 @@ resample()
2019-01-01
0.5547
- 0.168815
+ 0.183983
2020-01-01
0.5547
- 0.171846
+ 0.121213
@@ -2332,7 +2332,7 @@ 変化率の計算
-<pandas.core.groupby.generic.DataFrameGroupBy object at 0x11c9f0290>
+<pandas.core.groupby.generic.DataFrameGroupBy object at 0x110cd8200>
@@ -2347,7 +2347,7 @@ 変化率の計算
-<pandas.core.groupby.generic.SeriesGroupBy object at 0x11c9f3710>
+<pandas.core.groupby.generic.SeriesGroupBy object at 0x110f93e60>
diff --git a/13_random_TFP.html b/13_random_TFP.html
index b14bf530..6be35e1d 100644
--- a/13_random_TFP.html
+++ b/13_random_TFP.html
@@ -587,7 +587,7 @@ 平均と分散
-
+
２つの特徴がある。
@@ -603,7 +603,7 @@ 平均と分散
-(-0.0713458438036476, 0.8404674850814047)
+(-0.04116827681884658, 1.1586194464746402)
@@ -618,7 +618,7 @@ 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いる。これは分散が一定であるためである。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。
@@ -659,28 +659,28 @@ 自己共分散（自己相関）
-
+
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。
@@ -716,7 +716,7 @@ 自己共分散（自己相関）
-
+
インフレ率と失業率#
次に、失業率とインフレ率の持続性を確認する。
各変数の乖離を計算するが、注意する点がある。GDPなどの変数と違い、インフレ率と失業率は長期的なトレンドはない。従って、式(101)を使い、対数化せずに計算する必要がる。
@@ -2337,8 +2337,8 @@ インフレ率と失業率
-
インフレ率と失業率
-変動の大きさ#
+
+変動の大きさ#
次に変動の大きさを考えるために，GDPの標準偏差に対するそれぞれの構成要素の標準偏差の比率を計算しよう。
diff --git a/11_Macro_Variables.html b/11_Macro_Variables.html
index 02c99fa4..1e422227 100644
--- a/11_Macro_Variables.html
+++ b/11_Macro_Variables.html
@@ -732,7 +732,7 @@ 回帰分析#
Model: OLS Adj. R-squared: 0.387
Method: Least Squares F-statistic: 111.5
Date: Sat, 17 Aug 2024 Prob (F-statistic): 1.84e-20
-Time: 01:23:12 Log-Likelihood: -275.03
+Time: 01:39:52 Log-Likelihood: -275.03
No. Observations: 176 AIC: 554.1
Df Residuals: 174 BIC: 560.4
Df Model: 1
@@ -1317,122 +1317,122 @@ resample()
2019-01-01
10
- 4.960362
+ 6.398947
2019-02-01
20
- 5.211487
+ 4.601473
2019-03-01
30
- 6.066279
+ 4.155280
2019-04-01
40
- 6.307194
+ 4.043636
2019-05-01
50
- 6.421642
+ 4.871667
2019-06-01
60
- 6.324687
+ 5.474436
2019-07-01
70
- 5.219173
+ 5.469829
2019-08-01
80
- 3.876284
+ 5.683622
2019-09-01
90
- 3.997646
+ 5.425678
2019-10-01
100
- 5.987195
+ 4.573360
2019-11-01
110
- 4.783851
+ 6.808362
2019-12-01
120
- 4.686246
+ 3.761755
2020-01-01
10
- 4.811122
+ 4.959200
2020-02-01
20
- 4.960091
+ 3.975104
2020-03-01
30
- 4.712852
+ 5.494370
2020-04-01
40
- 4.745662
+ 5.606324
2020-05-01
50
- 5.217352
+ 5.247615
2020-06-01
60
- 3.446441
+ 5.696802
2020-07-01
70
- 4.974370
+ 5.252175
2020-08-01
80
- 3.999436
+ 5.706897
2020-09-01
90
- 5.855918
+ 5.429330
2020-10-01
100
- 6.453502
+ 3.853960
2020-11-01
110
- 5.557520
+ 5.387163
2020-12-01
120
- 3.946524
+ 4.893141
@@ -1460,7 +1460,7 @@ resample()
-<pandas.core.resample.DatetimeIndexResampler object at 0x11cea8f80>
+<pandas.core.resample.DatetimeIndexResampler object at 0x110ee56d0>
@@ -1501,42 +1501,42 @@ resample()
2019-01-01
20.0
- 5.412709
+ 5.051900
2019-04-01
50.0
- 6.351174
+ 4.796580
2019-07-01
80.0
- 4.364368
+ 5.526376
2019-10-01
110.0
- 5.152431
+ 5.047826
2020-01-01
20.0
- 4.828021
+ 4.809558
2020-04-01
50.0
- 4.469819
+ 5.516914
2020-07-01
80.0
- 4.943241
+ 5.462801
2020-10-01
110.0
- 5.319182
+ 4.711421
@@ -1577,12 +1577,12 @@ resample()
2019-01-01
65.0
- 5.320170
+ 5.105670
2020-01-01
65.0
- 4.890066
+ 5.125174
@@ -1667,12 +1667,12 @@ resample()
2019-01-01
0.5547
- 0.168815
+ 0.183983
2020-01-01
0.5547
- 0.171846
+ 0.121213
@@ -2332,7 +2332,7 @@ 変化率の計算
-<pandas.core.groupby.generic.DataFrameGroupBy object at 0x11c9f0290>
+<pandas.core.groupby.generic.DataFrameGroupBy object at 0x110cd8200>
@@ -2347,7 +2347,7 @@ 変化率の計算
-<pandas.core.groupby.generic.SeriesGroupBy object at 0x11c9f3710>
+<pandas.core.groupby.generic.SeriesGroupBy object at 0x110f93e60>
diff --git a/13_random_TFP.html b/13_random_TFP.html
index b14bf530..6be35e1d 100644
--- a/13_random_TFP.html
+++ b/13_random_TFP.html
@@ -587,7 +587,7 @@ 平均と分散
-
+
２つの特徴がある。
@@ -603,7 +603,7 @@ 平均と分散
-(-0.0713458438036476, 0.8404674850814047)
+(-0.04116827681884658, 1.1586194464746402)
@@ -618,7 +618,7 @@ 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いる。これは分散が一定であるためである。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。
@@ -659,28 +659,28 @@ 自己共分散（自己相関）
-
+
変動の大きさ#
次に変動の大きさを考えるために，GDPの標準偏差に対するそれぞれの構成要素の標準偏差の比率を計算しよう。
diff --git a/11_Macro_Variables.html b/11_Macro_Variables.html
index 02c99fa4..1e422227 100644
--- a/11_Macro_Variables.html
+++ b/11_Macro_Variables.html
@@ -732,7 +732,7 @@ 回帰分析#
Model: OLS Adj. R-squared: 0.387
Method: Least Squares F-statistic: 111.5
Date: Sat, 17 Aug 2024 Prob (F-statistic): 1.84e-20
-Time: 01:23:12 Log-Likelihood: -275.03
+Time: 01:39:52 Log-Likelihood: -275.03
No. Observations: 176 AIC: 554.1
Df Residuals: 174 BIC: 560.4
Df Model: 1
@@ -1317,122 +1317,122 @@
回帰分析#
Model: OLS Adj. R-squared: 0.387
Method: Least Squares F-statistic: 111.5
Date: Sat, 17 Aug 2024 Prob (F-statistic): 1.84e-20
-Time: 01:23:12 Log-Likelihood: -275.03
+Time: 01:39:52 Log-Likelihood: -275.03
No. Observations: 176 AIC: 554.1
Df Residuals: 174 BIC: 560.4
Df Model: 1
@@ -1317,122 +1317,122 @@ resample()
2019-01-01
10
- 4.960362
+ 6.398947
2019-02-01
20
- 5.211487
+ 4.601473
2019-03-01
30
- 6.066279
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2019-04-01
40
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2019-05-01
50
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2019-06-01
60
- 6.324687
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2019-07-01
70
- 5.219173
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2019-08-01
80
- 3.876284
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2019-09-01
90
- 3.997646
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2019-10-01
100
- 5.987195
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2019-11-01
110
- 4.783851
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2019-12-01
120
- 4.686246
+ 3.761755
2020-01-01
10
- 4.811122
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20
- 4.960091
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2020-03-01
30
- 4.712852
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40
- 4.745662
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2020-05-01
50
- 5.217352
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60
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2020-07-01
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2020-08-01
80
- 3.999436
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2020-09-01
90
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2020-10-01
100
- 6.453502
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2020-11-01
110
- 5.557520
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2020-12-01
120
- 3.946524
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@@ -1460,7 +1460,7 @@ resample()
resample()
2019-01-01
10
- 4.960362
+ 6.398947
2019-02-01
20
- 5.211487
+ 4.601473
2019-03-01
30
- 6.066279
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50
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70
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80
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90
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100
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110
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120
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10
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2020-02-01
20
- 4.960091
+ 3.975104
2020-03-01
30
- 4.712852
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2020-04-01
40
- 4.745662
+ 5.606324
2020-05-01
50
- 5.217352
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60
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70
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2020-08-01
80
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2020-09-01
90
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2020-10-01
100
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2020-11-01
110
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2020-12-01
120
- 3.946524
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@@ -1460,7 +1460,7 @@ resample()
-
@@ -1501,42 +1501,42 @@
自己共分散（自己相関）
-
<pandas.core.resample.DatetimeIndexResampler object at 0x11cea8f80>
+<pandas.core.resample.DatetimeIndexResampler object at 0x110ee56d0>
resample()
2019-01-01
20.0
- 5.412709
+ 5.051900
2019-04-01
50.0
- 6.351174
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2019-07-01
80.0
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2019-10-01
110.0
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2020-01-01
20.0
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2020-04-01
50.0
- 4.469819
+ 5.516914
2020-07-01
80.0
- 4.943241
+ 5.462801
2020-10-01
110.0
- 5.319182
+ 4.711421
@@ -1577,12 +1577,12 @@ resample()
2019-01-01
65.0
- 5.320170
+ 5.105670
2020-01-01
65.0
- 4.890066
+ 5.125174
@@ -1667,12 +1667,12 @@ resample()
2019-01-01
0.5547
- 0.168815
+ 0.183983
2020-01-01
0.5547
- 0.171846
+ 0.121213
@@ -2332,7 +2332,7 @@ 変化率の計算
-<pandas.core.groupby.generic.DataFrameGroupBy object at 0x11c9f0290>
+<pandas.core.groupby.generic.DataFrameGroupBy object at 0x110cd8200>
@@ -2347,7 +2347,7 @@ 変化率の計算
-<pandas.core.groupby.generic.SeriesGroupBy object at 0x11c9f3710>
+<pandas.core.groupby.generic.SeriesGroupBy object at 0x110f93e60>
diff --git a/13_random_TFP.html b/13_random_TFP.html
index b14bf530..6be35e1d 100644
--- a/13_random_TFP.html
+++ b/13_random_TFP.html
@@ -587,7 +587,7 @@ 平均と分散
-
+
２つの特徴がある。
@@ -603,7 +603,7 @@ 平均と分散
-(-0.0713458438036476, 0.8404674850814047)
+(-0.04116827681884658, 1.1586194464746402)
@@ -618,7 +618,7 @@ 平均と分散
-
+
resample()
2019-01-01
65.0
- 5.320170
+ 5.105670
2020-01-01
65.0
- 4.890066
+ 5.125174
@@ -1667,12 +1667,12 @@ resample()
2019-01-01
0.5547
- 0.168815
+ 0.183983
2020-01-01
0.5547
- 0.171846
+ 0.121213
@@ -2332,7 +2332,7 @@ 変化率の計算
-<pandas.core.groupby.generic.DataFrameGroupBy object at 0x11c9f0290>
+<pandas.core.groupby.generic.DataFrameGroupBy object at 0x110cd8200>
@@ -2347,7 +2347,7 @@ 変化率の計算
-<pandas.core.groupby.generic.SeriesGroupBy object at 0x11c9f3710>
+<pandas.core.groupby.generic.SeriesGroupBy object at 0x110f93e60>
diff --git a/13_random_TFP.html b/13_random_TFP.html
index b14bf530..6be35e1d 100644
--- a/13_random_TFP.html
+++ b/13_random_TFP.html
@@ -587,7 +587,7 @@ 平均と分散
-
+
２つの特徴がある。
@@ -603,7 +603,7 @@ 平均と分散
-(-0.0713458438036476, 0.8404674850814047)
+(-0.04116827681884658, 1.1586194464746402)
@@ -618,7 +618,7 @@ 平均と分散
-
+
resample()
2019-01-01
0.5547
- 0.168815
+ 0.183983
2020-01-01
0.5547
- 0.171846
+ 0.121213
@@ -2332,7 +2332,7 @@ 変化率の計算
-<pandas.core.groupby.generic.DataFrameGroupBy object at 0x11c9f0290>
+<pandas.core.groupby.generic.DataFrameGroupBy object at 0x110cd8200>
@@ -2347,7 +2347,7 @@ 変化率の計算
-<pandas.core.groupby.generic.SeriesGroupBy object at 0x11c9f3710>
+<pandas.core.groupby.generic.SeriesGroupBy object at 0x110f93e60>
diff --git a/13_random_TFP.html b/13_random_TFP.html
index b14bf530..6be35e1d 100644
--- a/13_random_TFP.html
+++ b/13_random_TFP.html
@@ -587,7 +587,7 @@ 平均と分散
-
+
２つの特徴がある。
@@ -603,7 +603,7 @@ 平均と分散
-(-0.0713458438036476, 0.8404674850814047)
+(-0.04116827681884658, 1.1586194464746402)
@@ -618,7 +618,7 @@ 平均と分散
-
+
変化率の計算
-<pandas.core.groupby.generic.DataFrameGroupBy object at 0x11c9f0290>
+<pandas.core.groupby.generic.DataFrameGroupBy object at 0x110cd8200>
@@ -2347,7 +2347,7 @@ 変化率の計算
-<pandas.core.groupby.generic.SeriesGroupBy object at 0x11c9f3710>
+<pandas.core.groupby.generic.SeriesGroupBy object at 0x110f93e60>
diff --git a/13_random_TFP.html b/13_random_TFP.html
index b14bf530..6be35e1d 100644
--- a/13_random_TFP.html
+++ b/13_random_TFP.html
@@ -587,7 +587,7 @@ 平均と分散
-
+
２つの特徴がある。
@@ -603,7 +603,7 @@ 平均と分散
-(-0.0713458438036476, 0.8404674850814047)
+(-0.04116827681884658, 1.1586194464746402)
@@ -618,7 +618,7 @@ 平均と分散
-
+
<pandas.core.groupby.generic.DataFrameGroupBy object at 0x11c9f0290>
+<pandas.core.groupby.generic.DataFrameGroupBy object at 0x110cd8200>
変化率の計算
-<pandas.core.groupby.generic.SeriesGroupBy object at 0x11c9f3710>
+<pandas.core.groupby.generic.SeriesGroupBy object at 0x110f93e60>
diff --git a/13_random_TFP.html b/13_random_TFP.html
index b14bf530..6be35e1d 100644
--- a/13_random_TFP.html
+++ b/13_random_TFP.html
@@ -587,7 +587,7 @@ 平均と分散
-
+
<pandas.core.groupby.generic.SeriesGroupBy object at 0x11c9f3710>
+<pandas.core.groupby.generic.SeriesGroupBy object at 0x110f93e60>
平均と分散
-
+
(-0.0713458438036476, 0.8404674850814047)
+(-0.04116827681884658, 1.1586194464746402)
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いる。これは分散が一定であるためである。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（自己相関）
-
+
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。
@@ -716,7 +716,7 @@自己共分散（自己相関）
-
+
-
@@ -757,13 +757,13 @@
自己共分散（自己相関）
--0.12034695272500617
+-0.045767970182586284
@@ -818,11 +818,11 @@ 自己共分散（自己相関）
--0.12034695272500617
+-0.04576797018258628
@@ -938,7 +938,7 @@ 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。
@@ -949,7 +949,7 @@ ３つの例：持続性の違い
-
+
-0.12034695272500617
+-0.045767970182586284
自己共分散（自己相関）
--0.12034695272500617
+-0.04576797018258628
@@ -938,7 +938,7 @@ ３つの例：持続性の違い
-
+
-0.12034695272500617
+-0.04576797018258628
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。
@@ -960,7 +960,7 @@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。
@@ -1498,10 +1498,10 @@ AR(1)としてのTFP
-自己相関係数：0.518
+自己相関係数：0.509
-
+
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。
@@ -1883,92 +1883,92 @@ 実行#<
272071.676745
212986.674833
59085.001912
- 13.691691
- -0.038636
- 0.003670
- -0.003670
- 12.531400
- -0.017579
- 12.286564
- -0.017579
- 11.004312
- -0.017579
+ 13.692113
+ -0.039058
+ 0.004269
+ -0.004269
+ 12.532150
+ -0.018329
+ 12.287314
+ -0.018329
+ 11.005062
+ -0.018329
1
8.878873e+05
- 1.016391
+ 0.997289
0.367161
- 281580.370237
- 220430.393463
- 61149.976774
- 13.724794
- -0.028194
- 0.003451
- 0.012807
- 12.545516
- 0.002657
- 12.300680
- 0.002657
- 11.018428
- 0.002657
+ 276288.561189
+ 216287.790945
+ 60000.770244
+ 13.725127
+ -0.028527
+ 0.003733
+ -0.006447
+ 12.545918
+ -0.016717
+ 12.301082
+ -0.016717
+ 11.018830
+ -0.016717
2
- 9.268401e+05
- 1.001846
+ 9.256909e+05
+ 1.012529
0.368050
- 282556.810896
- 221194.783390
- 61362.027506
- 13.757873
- -0.018336
- 0.003229
- -0.001385
- 12.559621
- -0.007986
- 12.314785
- -0.007986
- 11.032533
- -0.007986
+ 285442.333347
+ 223453.665458
+ 61988.667889
+ 13.758118
+ -0.019822
+ 0.003194
+ 0.009257
+ 12.559674
+ 0.002121
+ 12.314838
+ 0.002121
+ 11.032586
+ 0.002121
3
- 9.650311e+05
- 0.994857
+ 9.645373e+05
+ 1.017516
0.368942
- 285383.598424
- 223407.685825
- 61975.912599
- 13.790886
- -0.010970
- 0.003011
- -0.008167
- 12.573706
- -0.012117
- 12.328870
- -0.012117
- 11.046618
- -0.012117
+ 291829.688172
+ 228453.897314
+ 63375.790858
+ 13.791041
+ -0.011637
+ 0.002646
+ 0.014718
+ 12.573397
+ 0.010528
+ 12.328561
+ 0.010528
+ 11.046309
+ 0.010528
4
- 1.002881e+06
- 0.999726
+ 1.003800e+06
+ 1.011192
0.369835
- 291483.836669
- 228183.153360
- 63300.683309
- 13.823780
- -0.005392
- 0.002801
- -0.003075
- 12.587756
- -0.005017
- 12.342920
- -0.005017
- 11.060668
- -0.005017
+ 294924.192654
+ 230876.377404
+ 64047.815250
+ 13.823843
+ -0.004540
+ 0.002088
+ 0.009042
+ 12.587066
+ 0.007407
+ 12.342230
+ 0.007407
+ 11.059978
+ 0.007407
@@ -1984,7 +1984,7 @@ 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。
@@ -1998,7 +1998,7 @@ 実行#<
-
+
絶対値で約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。
@@ -2022,11 +2022,11 @@ 結果#<
--- シミュレーション：変動の自己相関係数 ---
-Yの変動： 0.467
-Cの変動： 0.467
-Iの変動： 0.467
+Yの変動： 0.480
+Cの変動： 0.480
+Iの変動： 0.480
Kの変動： 0.971
-Aの変動： 0.458
+Aの変動： 0.464
@@ -2104,8 +2104,8 @@ 結果#<
Cの変動： 1.000
Iの変動： 1.000
-Kの変動： 0.152
-Aの変動： 0.980
+Kの変動： 0.194
+Aの変動： 0.977
diff --git a/18_ADAS-1.html b/18_ADAS-1.html
index 59d9bbce..e6f05ce7 100644
--- a/18_ADAS-1.html
+++ b/18_ADAS-1.html
@@ -1242,7 +1242,7 @@ 準備：\(h\)の推定値
Model: OLS Adj. R-squared: 0.688
Method: Least Squares F-statistic: 384.1
Date: Sat, 17 Aug 2024 Prob (F-statistic): 8.56e-46
-Time: 01:23:31 Log-Likelihood: 716.66
+Time: 01:40:10 Log-Likelihood: 716.66
No. Observations: 175 AIC: -1429.
Df Residuals: 173 BIC: -1423.
Df Model: 1
@@ -1315,7 +1315,7 @@ 最初のスイッチ：\(c\)プロット
-
+
\(u_t\)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。
@@ -1129,7 +1129,7 @@
プロット
-
+
このプロットから次の点を確認できる。
@@ -1183,8 +1183,8 @@ GDPと価格水準の％乖離の標準偏差
-yの標準偏差:0.01378
-pの標準偏差:0.01407
+yの標準偏差:0.01382
+pの標準偏差:0.01417
@@ -1234,8 +1234,8 @@ 自己相関係数
-y:0.049
-p:0.816
+y:0.046
+p:0.819
@@ -1281,7 +1281,7 @@ p
--0.10823056996603567
+-0.11134686677389267
@@ -1312,11 +1312,11 @@ 結果のまとめと拡張-0.15298
WNショック
0.01378
0.01407
0.04896
0.81570
-0.10823
0.01382
0.01417
0.04645
0.81881
-0.11135
AR(1)ショック
0.01252
回帰分析#
Model: OLS Adj. R-squared: 0.848
Method: Least Squares F-statistic: 336.7
Date: Sat, 17 Aug 2024 Prob (F-statistic): 4.64e-26
-Time: 01:23:56 Log-Likelihood: 49.767
+Time: 01:40:31 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/10_Data_Fluctuation.ipynb b/_sources/10_Data_Fluctuation.ipynb
index be3038cb..e015b87a 100644
--- a/_sources/10_Data_Fluctuation.ipynb
+++ b/_sources/10_Data_Fluctuation.ipynb
@@ -1732,7 +1732,7 @@
"jp-MarkdownHeadingCollapsed": true
},
"source": [
- "### GDPの場合"
+ "### `.cov`と`.corr()`と`.autocorr()`：GDPの場合"
]
},
{
diff --git a/_sources/index.ipynb b/_sources/index.ipynb
index 38718a83..a1cd263a 100644
--- a/_sources/index.ipynb
+++ b/_sources/index.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "24c59d9a",
+ "id": "dc79dbdb",
"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": "9e05c22a",
+ "id": "a81d7325",
"metadata": {},
"outputs": [
{
@@ -41,7 +41,7 @@
},
{
"cell_type": "markdown",
- "id": "d29cfad3",
+ "id": "9192cfda",
"metadata": {},
"source": [
"
自己相関係数：0.518
+自己相関係数：0.509
-
+
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。
@@ -1883,92 +1883,92 @@実行#<
272071.676745
212986.674833
59085.001912
- 13.691691
- -0.038636
- 0.003670
- -0.003670
- 12.531400
- -0.017579
- 12.286564
- -0.017579
- 11.004312
- -0.017579
+ 13.692113
+ -0.039058
+ 0.004269
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+ -0.018329
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+ -0.018329
+ 11.005062
+ -0.018329
1
8.878873e+05
- 1.016391
+ 0.997289
0.367161
- 281580.370237
- 220430.393463
- 61149.976774
- 13.724794
- -0.028194
- 0.003451
- 0.012807
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- 0.002657
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- 0.002657
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- 0.002657
+ 276288.561189
+ 216287.790945
+ 60000.770244
+ 13.725127
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+ 0.003733
+ -0.006447
+ 12.545918
+ -0.016717
+ 12.301082
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+ 11.018830
+ -0.016717
2
- 9.268401e+05
- 1.001846
+ 9.256909e+05
+ 1.012529
0.368050
- 282556.810896
- 221194.783390
- 61362.027506
- 13.757873
- -0.018336
- 0.003229
- -0.001385
- 12.559621
- -0.007986
- 12.314785
- -0.007986
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- -0.007986
+ 285442.333347
+ 223453.665458
+ 61988.667889
+ 13.758118
+ -0.019822
+ 0.003194
+ 0.009257
+ 12.559674
+ 0.002121
+ 12.314838
+ 0.002121
+ 11.032586
+ 0.002121
3
- 9.650311e+05
- 0.994857
+ 9.645373e+05
+ 1.017516
0.368942
- 285383.598424
- 223407.685825
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- 13.790886
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- 0.003011
- -0.008167
- 12.573706
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- -0.012117
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- -0.012117
+ 291829.688172
+ 228453.897314
+ 63375.790858
+ 13.791041
+ -0.011637
+ 0.002646
+ 0.014718
+ 12.573397
+ 0.010528
+ 12.328561
+ 0.010528
+ 11.046309
+ 0.010528
4
- 1.002881e+06
- 0.999726
+ 1.003800e+06
+ 1.011192
0.369835
- 291483.836669
- 228183.153360
- 63300.683309
- 13.823780
- -0.005392
- 0.002801
- -0.003075
- 12.587756
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- 12.342920
- -0.005017
- 11.060668
- -0.005017
+ 294924.192654
+ 230876.377404
+ 64047.815250
+ 13.823843
+ -0.004540
+ 0.002088
+ 0.009042
+ 12.587066
+ 0.007407
+ 12.342230
+ 0.007407
+ 11.059978
+ 0.007407
@@ -1984,7 +1984,7 @@ 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。
@@ -1998,7 +1998,7 @@実行#<
-
+
+
絶対値で約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。
@@ -2022,11 +2022,11 @@結果#<
--- シミュレーション：変動の自己相関係数 ---
-Yの変動： 0.467
-Cの変動： 0.467
-Iの変動： 0.467
+Yの変動： 0.480
+Cの変動： 0.480
+Iの変動： 0.480
Kの変動： 0.971
-Aの変動： 0.458
+Aの変動： 0.464
@@ -2104,8 +2104,8 @@ 結果#<
Cの変動： 1.000
Iの変動： 1.000
-Kの変動： 0.152
-Aの変動： 0.980
+Kの変動： 0.194
+Aの変動： 0.977
diff --git a/18_ADAS-1.html b/18_ADAS-1.html
index 59d9bbce..e6f05ce7 100644
--- a/18_ADAS-1.html
+++ b/18_ADAS-1.html
@@ -1242,7 +1242,7 @@ 準備：\(h\)の推定値
Model: OLS Adj. R-squared: 0.688
Method: Least Squares F-statistic: 384.1
Date: Sat, 17 Aug 2024 Prob (F-statistic): 8.56e-46
-Time: 01:23:31 Log-Likelihood: 716.66
+Time: 01:40:10 Log-Likelihood: 716.66
No. Observations: 175 AIC: -1429.
Df Residuals: 173 BIC: -1423.
Df Model: 1
@@ -1315,7 +1315,7 @@ 最初のスイッチ：\(c\)プロット
-
+
\(u_t\)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。
@@ -1129,7 +1129,7 @@
プロット
-
+
このプロットから次の点を確認できる。
@@ -1183,8 +1183,8 @@ GDPと価格水準の％乖離の標準偏差
-yの標準偏差:0.01378
-pの標準偏差:0.01407
+yの標準偏差:0.01382
+pの標準偏差:0.01417
@@ -1234,8 +1234,8 @@ 自己相関係数
-y:0.049
-p:0.816
+y:0.046
+p:0.819
@@ -1281,7 +1281,7 @@ p
--0.10823056996603567
+-0.11134686677389267
@@ -1312,11 +1312,11 @@ 結果のまとめと拡張-0.15298
WNショック
0.01378
0.01407
0.04896
0.81570
-0.10823
0.01382
0.01417
0.04645
0.81881
-0.11135
AR(1)ショック
0.01252
回帰分析#
Model: OLS Adj. R-squared: 0.848
Method: Least Squares F-statistic: 336.7
Date: Sat, 17 Aug 2024 Prob (F-statistic): 4.64e-26
-Time: 01:23:56 Log-Likelihood: 49.767
+Time: 01:40:31 Log-Likelihood: 49.767
No. Observations: 61 AIC: -95.53
Df Residuals: 59 BIC: -91.31
Df Model: 1
diff --git a/_images/05086a77e4c41700aa62375a7fbcaf58ac20c3245ab71859d4065c1abcabaa39.png b/_images/05086a77e4c41700aa62375a7fbcaf58ac20c3245ab71859d4065c1abcabaa39.png
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diff --git a/_images/fb31bcc330e05deff57977cd869ce472e99baf933bef26a4add25c83c695fe09.png b/_images/fb31bcc330e05deff57977cd869ce472e99baf933bef26a4add25c83c695fe09.png
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diff --git a/_sources/10_Data_Fluctuation.ipynb b/_sources/10_Data_Fluctuation.ipynb
index be3038cb..e015b87a 100644
--- a/_sources/10_Data_Fluctuation.ipynb
+++ b/_sources/10_Data_Fluctuation.ipynb
@@ -1732,7 +1732,7 @@
"jp-MarkdownHeadingCollapsed": true
},
"source": [
- "### GDPの場合"
+ "### `.cov`と`.corr()`と`.autocorr()`：GDPの場合"
]
},
{
diff --git a/_sources/index.ipynb b/_sources/index.ipynb
index 38718a83..a1cd263a 100644
--- a/_sources/index.ipynb
+++ b/_sources/index.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "24c59d9a",
+ "id": "dc79dbdb",
"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": "9e05c22a",
+ "id": "a81d7325",
"metadata": {},
"outputs": [
{
@@ -41,7 +41,7 @@
},
{
"cell_type": "markdown",
- "id": "d29cfad3",
+ "id": "9192cfda",
"metadata": {},
"source": [
"
--- シミュレーション：変動の自己相関係数 ---
-Yの変動： 0.467
-Cの変動： 0.467
-Iの変動： 0.467
+Yの変動： 0.480
+Cの変動： 0.480
+Iの変動： 0.480
Kの変動： 0.971
-Aの変動： 0.458
+Aの変動： 0.464
準備：\(h\)の推定値
Model: OLS Adj. R-squared: 0.688
Method: Least Squares F-statistic: 384.1
Date: Sat, 17 Aug 2024 Prob (F-statistic): 8.56e-46
-Time: 01:23:31 Log-Likelihood: 716.66
+Time: 01:40:10 Log-Likelihood: 716.66
No. Observations: 175 AIC: -1429.
Df Residuals: 173 BIC: -1423.
Df Model: 1
@@ -1315,7 +1315,7 @@ 最初のスイッチ：\(c\)プロット
-
+
\(u_t\)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。
@@ -1129,7 +1129,7 @@
プロット
-
+
このプロットから次の点を確認できる。
@@ -1183,8 +1183,8 @@ GDPと価格水準の％乖離の標準偏差
-yの標準偏差:0.01378
-pの標準偏差:0.01407
+yの標準偏差:0.01382
+pの標準偏差:0.01417
@@ -1234,8 +1234,8 @@ 自己相関係数
-y:0.049
-p:0.816
+y:0.046
+p:0.819
@@ -1281,7 +1281,7 @@ p
--0.10823056996603567
+-0.11134686677389267
@@ -1312,11 +1312,11 @@ 結果のまとめと拡張-0.15298
WNショック
0.01378
0.01407
0.04896
0.81570
-0.10823
0.01382
0.01417
0.04645
0.81881
-0.11135
AR(1)ショック
0.01252
回帰分析#
Model: OLS Adj. R-squared: 0.848
Method: Least Squares F-statistic: 336.7
Date: Sat, 17 Aug 2024 Prob (F-statistic): 4.64e-26
-Time: 01:23:56 Log-Likelihood: 49.767
+Time: 01:40:31 Log-Likelihood: 49.767
No. Observations: 61 AIC: -95.53
Df Residuals: 59 BIC: -91.31
Df Model: 1
diff --git a/_images/05086a77e4c41700aa62375a7fbcaf58ac20c3245ab71859d4065c1abcabaa39.png b/_images/05086a77e4c41700aa62375a7fbcaf58ac20c3245ab71859d4065c1abcabaa39.png
new file mode 100644
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diff --git a/_sources/10_Data_Fluctuation.ipynb b/_sources/10_Data_Fluctuation.ipynb
index be3038cb..e015b87a 100644
--- a/_sources/10_Data_Fluctuation.ipynb
+++ b/_sources/10_Data_Fluctuation.ipynb
@@ -1732,7 +1732,7 @@
"jp-MarkdownHeadingCollapsed": true
},
"source": [
- "### GDPの場合"
+ "### `.cov`と`.corr()`と`.autocorr()`：GDPの場合"
]
},
{
diff --git a/_sources/index.ipynb b/_sources/index.ipynb
index 38718a83..a1cd263a 100644
--- a/_sources/index.ipynb
+++ b/_sources/index.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "24c59d9a",
+ "id": "dc79dbdb",
"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": "9e05c22a",
+ "id": "a81d7325",
"metadata": {},
"outputs": [
{
@@ -41,7 +41,7 @@
},
{
"cell_type": "markdown",
- "id": "d29cfad3",
+ "id": "9192cfda",
"metadata": {},
"source": [
"
-
+
+
\(u_t\)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。 @@ -1129,7 +1129,7 @@
プロット
-
+
このプロットから次の点を確認できる。
@@ -1183,8 +1183,8 @@ GDPと価格水準の％乖離の標準偏差
-yの標準偏差:0.01378
-pの標準偏差:0.01407
+yの標準偏差:0.01382
+pの標準偏差:0.01417
@@ -1234,8 +1234,8 @@ 自己相関係数
-y:0.049
-p:0.816
+y:0.046
+p:0.819
@@ -1281,7 +1281,7 @@ p
--0.10823056996603567
+-0.11134686677389267
@@ -1312,11 +1312,11 @@ 結果のまとめと拡張-0.15298
WNショック
0.01378
0.01407
0.04896
0.81570
-0.10823
0.01382
0.01417
0.04645
0.81881
-0.11135
AR(1)ショック
0.01252
回帰分析#
Model: OLS Adj. R-squared: 0.848
Method: Least Squares F-statistic: 336.7
Date: Sat, 17 Aug 2024 Prob (F-statistic): 4.64e-26
-Time: 01:23:56 Log-Likelihood: 49.767
+Time: 01:40:31 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/10_Data_Fluctuation.ipynb b/_sources/10_Data_Fluctuation.ipynb
index be3038cb..e015b87a 100644
--- a/_sources/10_Data_Fluctuation.ipynb
+++ b/_sources/10_Data_Fluctuation.ipynb
@@ -1732,7 +1732,7 @@
"jp-MarkdownHeadingCollapsed": true
},
"source": [
- "### GDPの場合"
+ "### `.cov`と`.corr()`と`.autocorr()`：GDPの場合"
]
},
{
diff --git a/_sources/index.ipynb b/_sources/index.ipynb
index 38718a83..a1cd263a 100644
--- a/_sources/index.ipynb
+++ b/_sources/index.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "24c59d9a",
+ "id": "dc79dbdb",
"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": "9e05c22a",
+ "id": "a81d7325",
"metadata": {},
"outputs": [
{
@@ -41,7 +41,7 @@
},
{
"cell_type": "markdown",
- "id": "d29cfad3",
+ "id": "9192cfda",
"metadata": {},
"source": [
"
+
yの標準偏差:0.01378
-pの標準偏差:0.01407
+yの標準偏差:0.01382
+pの標準偏差:0.01417
自己相関係数
-y:0.049
-p:0.816
+y:0.046
+p:0.819
@@ -1281,7 +1281,7 @@ p
y:0.049
-p:0.816
+y:0.046
+p:0.819
p
-
@@ -1312,11 +1312,11 @@ 結果のまとめと拡張-0.15298
-0.10823056996603567
+-0.11134686677389267
結果のまとめと拡張-0.15298
WNショック
0.01378
0.01407
0.04896
0.81570
-0.10823
0.01382
0.01417
0.04645
0.81881
-0.11135
AR(1)ショック
0.01252
回帰分析#
Model: OLS Adj. R-squared: 0.848
Method: Least Squares F-statistic: 336.7
Date: Sat, 17 Aug 2024 Prob (F-statistic): 4.64e-26
-Time: 01:23:56 Log-Likelihood: 49.767
+Time: 01:40:31 Log-Likelihood: 49.767
No. Observations: 61 AIC: -95.53
Df Residuals: 59 BIC: -91.31
Df Model: 1
diff --git a/_images/05086a77e4c41700aa62375a7fbcaf58ac20c3245ab71859d4065c1abcabaa39.png b/_images/05086a77e4c41700aa62375a7fbcaf58ac20c3245ab71859d4065c1abcabaa39.png
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diff --git a/_sources/10_Data_Fluctuation.ipynb b/_sources/10_Data_Fluctuation.ipynb
index be3038cb..e015b87a 100644
--- a/_sources/10_Data_Fluctuation.ipynb
+++ b/_sources/10_Data_Fluctuation.ipynb
@@ -1732,7 +1732,7 @@
"jp-MarkdownHeadingCollapsed": true
},
"source": [
- "### GDPの場合"
+ "### `.cov`と`.corr()`と`.autocorr()`：GDPの場合"
]
},
{
diff --git a/_sources/index.ipynb b/_sources/index.ipynb
index 38718a83..a1cd263a 100644
--- a/_sources/index.ipynb
+++ b/_sources/index.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "24c59d9a",
+ "id": "dc79dbdb",
"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": "9e05c22a",
+ "id": "a81d7325",
"metadata": {},
"outputs": [
{
@@ -41,7 +41,7 @@
},
{
"cell_type": "markdown",
- "id": "d29cfad3",
+ "id": "9192cfda",
"metadata": {},
"source": [
"
WNショック
0.01378
0.01407
0.04896
0.81570
-0.10823
0.01382
0.01417
0.04645
0.81881
-0.11135
AR(1)ショック
0.01252