Python因果关系F检验理解

Question

我正在为我的平稳时间序列尝试格兰杰因果关系。我很难理解它的信心水平。

e.g.1:

grangercausalitytests(filter_df[['transform_y_x', 'transform_y_y']], maxlag=15)

gives result:

Granger Causality
number of lags (no zero) 1
ssr based F test:         F=3.7764  , p=0.0530  , df_denom=286, df_num=1
ssr based chi2 test:   chi2=3.8161  , p=0.0508  , df=1
likelihood ratio test: chi2=3.7911  , p=0.0515  , df=1
parameter F test:         F=3.7764  , p=0.0530  , df_denom=286, df_num=1

Granger Causality
number of lags (no zero) 2
ssr based F test:         F=2.1949  , p=0.1133  , df_denom=283, df_num=2
ssr based chi2 test:   chi2=4.4673  , p=0.1071  , df=2
likelihood ratio test: chi2=4.4330  , p=0.1090  , df=2
parameter F test:         F=2.1949  , p=0.1133  , df_denom=283, df_num=2

Granger Causality
number of lags (no zero) 3
ssr based F test:         F=7.5713  , p=0.0001  , df_denom=280, df_num=3
ssr based chi2 test:   chi2=23.2818 , p=0.0000  , df=3
likelihood ratio test: chi2=22.3856 , p=0.0001  , df=3
parameter F test:         F=7.5713  , p=0.0001  , df_denom=280, df_num=3

Granger Causality
number of lags (no zero) 4
ssr based F test:         F=2.3756  , p=0.0523  , df_denom=277, df_num=4
ssr based chi2 test:   chi2=9.8113  , p=0.0437  , df=4
likelihood ratio test: chi2=9.6467  , p=0.0468  , df=4
parameter F test:         F=2.3756  , p=0.0523  , df_denom=277, df_num=4

Granger Causality
number of lags (no zero) 5
ssr based F test:         F=1.4871  , p=0.1941  , df_denom=274, df_num=5
ssr based chi2 test:   chi2=7.7338  , p=0.1715  , df=5
likelihood ratio test: chi2=7.6307  , p=0.1778  , df=5
parameter F test:         F=1.4871  , p=0.1941  , df_denom=274, df_num=5

Granger Causality
number of lags (no zero) 6
ssr based F test:         F=1.2781  , p=0.2675  , df_denom=271, df_num=6
ssr based chi2 test:   chi2=8.0363  , p=0.2355  , df=6
likelihood ratio test: chi2=7.9247  , p=0.2437  , df=6
parameter F test:         F=1.2781  , p=0.2675  , df_denom=271, df_num=6

Granger Causality
number of lags (no zero) 7
ssr based F test:         F=1.7097  , p=0.1067  , df_denom=268, df_num=7
ssr based chi2 test:   chi2=12.6378 , p=0.0814  , df=7
likelihood ratio test: chi2=12.3637 , p=0.0892  , df=7
parameter F test:         F=1.7097  , p=0.1067  , df_denom=268, df_num=7

Granger Causality
number of lags (no zero) 8
ssr based F test:         F=1.4672  , p=0.1692  , df_denom=265, df_num=8
ssr based chi2 test:   chi2=12.4909 , p=0.1306  , df=8
likelihood ratio test: chi2=12.2222 , p=0.1416  , df=8
parameter F test:         F=1.4672  , p=0.1692  , df_denom=265, df_num=8

Granger Causality
number of lags (no zero) 9
ssr based F test:         F=2.0761  , p=0.0320  , df_denom=262, df_num=9
ssr based chi2 test:   chi2=20.0400 , p=0.0177  , df=9
likelihood ratio test: chi2=19.3576 , p=0.0223  , df=9
parameter F test:         F=2.0761  , p=0.0320  , df_denom=262, df_num=9

Granger Causality
number of lags (no zero) 10
ssr based F test:         F=1.8313  , p=0.0556  , df_denom=259, df_num=10
ssr based chi2 test:   chi2=19.7977 , p=0.0312  , df=10
likelihood ratio test: chi2=19.1291 , p=0.0387  , df=10
parameter F test:         F=1.8313  , p=0.0556  , df_denom=259, df_num=10

Granger Causality
number of lags (no zero) 11
ssr based F test:         F=1.8893  , p=0.0410  , df_denom=256, df_num=11
ssr based chi2 test:   chi2=22.6493 , p=0.0198  , df=11
likelihood ratio test: chi2=21.7769 , p=0.0262  , df=11
parameter F test:         F=1.8893  , p=0.0410  , df_denom=256, df_num=11

Granger Causality
number of lags (no zero) 12
ssr based F test:         F=2.0157  , p=0.0234  , df_denom=253, df_num=12
ssr based chi2 test:   chi2=26.5779 , p=0.0089  , df=12
likelihood ratio test: chi2=25.3830 , p=0.0131  , df=12
parameter F test:         F=2.0157  , p=0.0234  , df_denom=253, df_num=12

Granger Causality
number of lags (no zero) 13
ssr based F test:         F=1.8636  , p=0.0347  , df_denom=250, df_num=13
ssr based chi2 test:   chi2=26.8434 , p=0.0131  , df=13
likelihood ratio test: chi2=25.6211 , p=0.0191  , df=13
parameter F test:         F=1.8636  , p=0.0347  , df_denom=250, df_num=13

Granger Causality
number of lags (no zero) 14
ssr based F test:         F=1.5283  , p=0.1013  , df_denom=247, df_num=14
ssr based chi2 test:   chi2=23.9090 , p=0.0470  , df=14
likelihood ratio test: chi2=22.9296 , p=0.0614  , df=14
parameter F test:         F=1.5283  , p=0.1013  , df_denom=247, df_num=14

Granger Causality
number of lags (no zero) 15
ssr based F test:         F=0.9749  , p=0.4823  , df_denom=244, df_num=15
ssr based chi2 test:   chi2=16.4815 , p=0.3508  , df=15
likelihood ratio test: chi2=16.0065 , p=0.3816  , df=15
parameter F test:         F=0.9749  , p=0.4823  , df_denom=244, df_num=15

和e.g2:

grangercausalitytests(filter_df[['transform_y_y', 'transform_y_x']], maxlag=15)

it says:
Granger Causality
number of lags (no zero) 1
ssr based F test:         F=70.4932 , p=0.0000  , df_denom=286, df_num=1
ssr based chi2 test:   chi2=71.2326 , p=0.0000  , df=1
likelihood ratio test: chi2=63.6734 , p=0.0000  , df=1
parameter F test:         F=70.4932 , p=0.0000  , df_denom=286, df_num=1

Granger Causality
number of lags (no zero) 2
ssr based F test:         F=47.3519 , p=0.0000  , df_denom=283, df_num=2
ssr based chi2 test:   chi2=96.3771 , p=0.0000  , df=2
likelihood ratio test: chi2=83.1351 , p=0.0000  , df=2
parameter F test:         F=47.3519 , p=0.0000  , df_denom=283, df_num=2

Granger Causality
number of lags (no zero) 3
ssr based F test:         F=33.6081 , p=0.0000  , df_denom=280, df_num=3
ssr based chi2 test:   chi2=103.3450, p=0.0000  , df=3
likelihood ratio test: chi2=88.2665 , p=0.0000  , df=3
parameter F test:         F=33.6081 , p=0.0000  , df_denom=280, df_num=3

Granger Causality
number of lags (no zero) 4
ssr based F test:         F=24.1709 , p=0.0000  , df_denom=277, df_num=4
ssr based chi2 test:   chi2=99.8248 , p=0.0000  , df=4
likelihood ratio test: chi2=85.6260 , p=0.0000  , df=4
parameter F test:         F=24.1709 , p=0.0000  , df_denom=277, df_num=4

Granger Causality
number of lags (no zero) 5
ssr based F test:         F=15.6663 , p=0.0000  , df_denom=274, df_num=5
ssr based chi2 test:   chi2=81.4760 , p=0.0000  , df=5
likelihood ratio test: chi2=71.6615 , p=0.0000  , df=5
parameter F test:         F=15.6663 , p=0.0000  , df_denom=274, df_num=5

Granger Causality
number of lags (no zero) 6
ssr based F test:         F=11.5874 , p=0.0000  , df_denom=271, df_num=6
ssr based chi2 test:   chi2=72.8595 , p=0.0000  , df=6
likelihood ratio test: chi2=64.8565 , p=0.0000  , df=6
parameter F test:         F=11.5874 , p=0.0000  , df_denom=271, df_num=6

Granger Causality
number of lags (no zero) 7
ssr based F test:         F=9.7282  , p=0.0000  , df_denom=268, df_num=7
ssr based chi2 test:   chi2=71.9090 , p=0.0000  , df=7
likelihood ratio test: chi2=64.0753 , p=0.0000  , df=7
parameter F test:         F=9.7282  , p=0.0000  , df_denom=268, df_num=7

Granger Causality
number of lags (no zero) 8
ssr based F test:         F=8.3121  , p=0.0000  , df_denom=265, df_num=8
ssr based chi2 test:   chi2=70.7626 , p=0.0000  , df=8
likelihood ratio test: chi2=63.1365 , p=0.0000  , df=8
parameter F test:         F=8.3121  , p=0.0000  , df_denom=265, df_num=8

Granger Causality
number of lags (no zero) 9
ssr based F test:         F=7.7863  , p=0.0000  , df_denom=262, df_num=9
ssr based chi2 test:   chi2=75.1583 , p=0.0000  , df=9
likelihood ratio test: chi2=66.6028 , p=0.0000  , df=9
parameter F test:         F=7.7863  , p=0.0000  , df_denom=262, df_num=9

Granger Causality
number of lags (no zero) 10
ssr based F test:         F=6.9230  , p=0.0000  , df_denom=259, df_num=10
ssr based chi2 test:   chi2=74.8427 , p=0.0000  , df=10
likelihood ratio test: chi2=66.3278 , p=0.0000  , df=10
parameter F test:         F=6.9230  , p=0.0000  , df_denom=259, df_num=10

Granger Causality
number of lags (no zero) 11
ssr based F test:         F=6.7168  , p=0.0000  , df_denom=256, df_num=11
ssr based chi2 test:   chi2=80.5233 , p=0.0000  , df=11
likelihood ratio test: chi2=70.7452 , p=0.0000  , df=11
parameter F test:         F=6.7168  , p=0.0000  , df_denom=256, df_num=11

Granger Causality
number of lags (no zero) 12
ssr based F test:         F=6.8729  , p=0.0000  , df_denom=253, df_num=12
ssr based chi2 test:   chi2=90.6239 , p=0.0000  , df=12
likelihood ratio test: chi2=78.4393 , p=0.0000  , df=12
parameter F test:         F=6.8729  , p=0.0000  , df_denom=253, df_num=12

Granger Causality
number of lags (no zero) 13
ssr based F test:         F=6.0868  , p=0.0000  , df_denom=250, df_num=13
ssr based chi2 test:   chi2=87.6748 , p=0.0000  , df=13
likelihood ratio test: chi2=76.1718 , p=0.0000  , df=13
parameter F test:         F=6.0868  , p=0.0000  , df_denom=250, df_num=13

Granger Causality
number of lags (no zero) 14
ssr based F test:         F=5.6246  , p=0.0000  , df_denom=247, df_num=14
ssr based chi2 test:   chi2=87.9896 , p=0.0000  , df=14
likelihood ratio test: chi2=76.3759 , p=0.0000  , df=14
parameter F test:         F=5.6246  , p=0.0000  , df_denom=247, df_num=14

Granger Causality
number of lags (no zero) 15
ssr based F test:         F=5.3775  , p=0.0000  , df_denom=244, df_num=15
ssr based chi2 test:   chi2=90.9098 , p=0.0000  , df=15
likelihood ratio test: chi2=78.5443 , p=0.0000  , df=15
parameter F test:         F=5.3775  , p=0.0000  , df_denom=244, df_num=15

从极小的滞后数来看，p值低于0.05，

那么我可以说y_x格兰杰导致了y_y吗？

从eg.2开始，p值都是0.0000，所以y_y格兰杰会导致x_y？

也就是说因果关系是双向的？

如何给格兰杰因果关系的信心评分？

F-测试值在这里起什么作用吗？

在eg.1中，所有的f测试值都很低，而eg.2都很高。在这种情况下，我能考虑F检验值得出结论吗？

如果是的话，那么F检验的重要价值是什么呢？

提亚

Answer 1

从eg.1的几个滞后，p值低于0.05，所以我可以说y_x格兰杰导致y_y吗？

从你的问题中，我假设你想把p值阈值设为0.05.在示例1中，对于number of lags (no zero) 1，当p值显示为p=0.0530时，这意味着y_y (第二列)的过去1值(滞后1)对y_x (第一列)的当前值没有显著影响。对于number of lags (no zero) 3，当p值显示为p=0.0001时，这意味着过去y_y (第二列)的3个值(联合)对y_x (第一列)的当前值有显著的统计意义。

从eg.2开始，p值都是0.0000，所以y_y格兰杰会导致y_x？

类似于上面的答案，在所有情况下，例如2，p-值<0.0 5，这意味着y_x (第二列)的过去值对y_y (第一列)的当前值有统计学意义的影响。

也就是说因果关系是双向的？

这取决于你想要解决的问题，典型的假设是因果关系是单向的。从您的结果来看，您似乎最有可能预测来自y_x的y_x值，而不是相反。如果输入信号具有相似的周期性，则可能会发现y_y的过去值与y_x的电流值之间存在微弱的相关性。

如何给格兰杰因果关系的信心评分？F-测试值在这里起什么作用吗？在eg.1中，所有的f测试值都很低，而eg.2都很高。在这种情况下，我能考虑F检验值得出结论吗？如果是的话，那么F检验的重要价值是什么呢？

基于自由度，F值和p值是相互关联的，因为您使用的是p值的阈值，这意味着您正在为F值设置一个阈值。

参考文献：

1. https://stats.stackexchange.com/questions/476536/interpreting-statsmodel-granger-causality-test-results-ssr-chi2test
2. 源代码
3. 格兰杰因果关系
4. F值计算器