Python格兰杰因果F检验理解
Python Granger Causality F test understanding
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 , 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 eg.1 几个滞后，p 值低于 0.05，
所以我可以说 y_x 格兰杰原因 y_y?
来自 eg.2，所有的 p 值都是 0.0000，
所以 y_y 格兰杰原因 x_y?
所以这意味着因果关系是双向的？
如何给出格兰杰因果关系的置信度分数？
F 检验值在这里起作用吗？
在 eg.1 中，所有的 f 检验值都非常低，而 eg.2 中的所有值都非常高。
在这种情况下，我是否可以考虑F检验值得出结论？
如果是这样，那么 F 检验要考虑的重要价值是什么？
TIA
from the eg.1 few lags, p-values are below 0.05,
so can I say y_x Granger causes y_y?
根据你的问题，我假设你想将 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 个值（滞后 1）对当前没有统计显着影响值为 y_x（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（联合）对 [= 的当前值具有统计显着影响43=]（第一列）。
from the eg.2, all are the p-values are 0.0000, so y_y Granger causes y_x?
与上述答案类似，在所有情况下，例如 2，p 值 < 0.05，这意味着 y_x（第二列）的过去值对 [=42= 的当前值具有统计显着影响]（第一列）。
so it means causation is bidirectional?
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信号，则可以看到 y_y 的过去值与 y_x.
的当前值之间的弱相关性
How to give a confidence score for the Granger Causation?
Does F-test value play any role here?
In eg.1 all the f-test values are very low and eg.2 all are very high. In this case, can I consider F-test values for arriving a conclusion?
if so, then what will be the significant value for F-test to consider?
根据自由度，F 值和 p 值相互关联，因为您使用的是 p 值的阈值，这意味着您正在为 F 值设置阈值。
参考文献：
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 , 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 eg.1 几个滞后，p 值低于 0.05，
所以我可以说 y_x 格兰杰原因 y_y?
来自 eg.2，所有的 p 值都是 0.0000，
所以 y_y 格兰杰原因 x_y?
所以这意味着因果关系是双向的？
如何给出格兰杰因果关系的置信度分数？
F 检验值在这里起作用吗？
在 eg.1 中，所有的 f 检验值都非常低，而 eg.2 中的所有值都非常高。
在这种情况下，我是否可以考虑F检验值得出结论？
如果是这样，那么 F 检验要考虑的重要价值是什么？
TIA
from the eg.1 few lags, p-values are below 0.05, so can I say y_x Granger causes y_y?
根据你的问题，我假设你想将 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 个值（滞后 1）对当前没有统计显着影响值为 y_x（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（联合）对 [= 的当前值具有统计显着影响43=]（第一列）。
from the eg.2, all are the p-values are 0.0000, so y_y Granger causes y_x?
与上述答案类似，在所有情况下，例如 2，p 值 < 0.05，这意味着 y_x（第二列）的过去值对 [=42= 的当前值具有统计显着影响]（第一列）。
so it means causation is bidirectional?
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信号，则可以看到 y_y 的过去值与 y_x.
的当前值之间的弱相关性How to give a confidence score for the Granger Causation? Does F-test value play any role here? In eg.1 all the f-test values are very low and eg.2 all are very high. In this case, can I consider F-test values for arriving a conclusion? if so, then what will be the significant value for F-test to consider?
根据自由度，F 值和 p 值相互关联，因为您使用的是 p 值的阈值，这意味着您正在为 F 值设置阈值。
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