如何解决Python Granger因果关系F测试理解
我正在为我的固定时间序列尝试格兰杰因果关系。我很难理解它的置信度。
对于例如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,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,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,df=3
parameter F test: F=7.5713,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,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,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,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,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,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,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,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,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,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,df=13
likelihood ratio test: chi2=25.6211,p=0.0191,df=13
parameter F test: F=1.8636,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,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,df_num=15
和 例如：
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,df_num=1
ssr based chi2 test: chi2=71.2326,df=1
likelihood ratio test: chi2=63.6734,df=1
parameter F test: F=70.4932,df_num=1
Granger Causality
number of lags (no zero) 2
ssr based F test: F=47.3519,df_num=2
ssr based chi2 test: chi2=96.3771,df=2
likelihood ratio test: chi2=83.1351,df=2
parameter F test: F=47.3519,df_num=2
Granger Causality
number of lags (no zero) 3
ssr based F test: F=33.6081,df_num=3
ssr based chi2 test: chi2=103.3450,df=3
likelihood ratio test: chi2=88.2665,df=3
parameter F test: F=33.6081,df_num=3
Granger Causality
number of lags (no zero) 4
ssr based F test: F=24.1709,df_num=4
ssr based chi2 test: chi2=99.8248,df=4
likelihood ratio test: chi2=85.6260,df=4
parameter F test: F=24.1709,df_num=4
Granger Causality
number of lags (no zero) 5
ssr based F test: F=15.6663,df_num=5
ssr based chi2 test: chi2=81.4760,df=5
likelihood ratio test: chi2=71.6615,df=5
parameter F test: F=15.6663,df_num=5
Granger Causality
number of lags (no zero) 6
ssr based F test: F=11.5874,df_num=6
ssr based chi2 test: chi2=72.8595,df=6
likelihood ratio test: chi2=64.8565,df=6
parameter F test: F=11.5874,df_num=6
Granger Causality
number of lags (no zero) 7
ssr based F test: F=9.7282,df_num=7
ssr based chi2 test: chi2=71.9090,df=7
likelihood ratio test: chi2=64.0753,df=7
parameter F test: F=9.7282,df_num=7
Granger Causality
number of lags (no zero) 8
ssr based F test: F=8.3121,df_num=8
ssr based chi2 test: chi2=70.7626,df=8
likelihood ratio test: chi2=63.1365,df=8
parameter F test: F=8.3121,df_num=8
Granger Causality
number of lags (no zero) 9
ssr based F test: F=7.7863,df_num=9
ssr based chi2 test: chi2=75.1583,df=9
likelihood ratio test: chi2=66.6028,df=9
parameter F test: F=7.7863,df_num=9
Granger Causality
number of lags (no zero) 10
ssr based F test: F=6.9230,df_num=10
ssr based chi2 test: chi2=74.8427,df=10
likelihood ratio test: chi2=66.3278,df=10
parameter F test: F=6.9230,df_num=10
Granger Causality
number of lags (no zero) 11
ssr based F test: F=6.7168,df_num=11
ssr based chi2 test: chi2=80.5233,df=11
likelihood ratio test: chi2=70.7452,df=11
parameter F test: F=6.7168,df_num=11
Granger Causality
number of lags (no zero) 12
ssr based F test: F=6.8729,df_num=12
ssr based chi2 test: chi2=90.6239,df=12
likelihood ratio test: chi2=78.4393,df=12
parameter F test: F=6.8729,df_num=12
Granger Causality
number of lags (no zero) 13
ssr based F test: F=6.0868,df_num=13
ssr based chi2 test: chi2=87.6748,df=13
likelihood ratio test: chi2=76.1718,df=13
parameter F test: F=6.0868,df_num=13
Granger Causality
number of lags (no zero) 14
ssr based F test: F=5.6246,df_num=14
ssr based chi2 test: chi2=87.9896,df=14
likelihood ratio test: chi2=76.3759,df=14
parameter F test: F=5.6246,df_num=14
Granger Causality
number of lags (no zero) 15
ssr based F test: F=5.3775,df_num=15
ssr based chi2 test: chi2=90.9098,df=15
likelihood ratio test: chi2=78.5443,df=15
parameter F test: F=5.3775,df_num=15
从 eg.1 几个滞后来看，p 值低于 0.05，
那么我可以说 y_x Granger 导致 y_y 吗？
从 eg.2，所有的 p 值都是 0.0000，
所以 y_y Granger 导致 x_y？
所以这意味着因果关系是双向的？
如何给格兰杰因果关系打分？
F-test 值在这里有什么作用吗？
在 eg.1 中，所有 f-test 值都非常低，而 eg.2 都非常高。
在这种情况下，我可以考虑 F 检验值来得出结论吗？
如果是这样，那么 F 检验要考虑的重要价值是什么？
TIA
解决方法
从 eg.1 几个滞后，p 值低于 0.05， 那么我可以说 y_x Granger 导致 y_y 吗？
根据您的问题，我假设您想将 p 值阈值设置为 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 的当前值没有统计显着影响（第一列）。对于 number of lags (no zero) 3，当 p 值显示为 p=0.0001 时，这意味着 y_y（第二列）的过去 3 个值（共同）对 y_x（第一列）的当前值具有统计显着影响。
从 eg.2，所有 p 值都是 0.0000，所以 y_y Granger 导致 y_x？
与上述答案类似，在所有情况下，例如 2，p 值
所以这意味着因果关系是双向的？
这取决于您要解决的问题，典型的假设是因果关系是单向的。从您的结果来看，您似乎最有可能从 y_x 预测 y_y 的值，而不是相反。如果两个输入信号都是具有相似周期性的循环，则可能会看到 y_y 的过去值和 y_x 的当前值之间存在弱相关性。
如何给出格兰杰因果关系的置信度？ F-test 值在这里有什么作用吗？ 在 eg.1 中，所有 f-test 值都非常低，而 eg.2 都非常高。在这种情况下，我可以考虑 F 检验值来得出结论吗？ 如果是这样，那么 F 检验要考虑的重要价值是什么？
根据自由度，F 值和 p 值相互关联，因为您使用的是 p 值阈值，这意味着您正在设置 F 值阈值。
参考文献：
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