我正在对我的平稳时间序列进行格兰杰因果检验。我很难理解它的置信水平。
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和例如2：
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从例如1的几个滞后，p值低于0.05，
我能说y_x格兰杰导致y_y吗
由方程2可知，所有的p值都是0.0000，所以y_y格兰杰导致x_y？
所以因果关系是双向的
如何给予格兰杰因果关系的置信度？
F检验值在这里起作用吗？
在例1中，所有的f检验值都很低，而例2中所有的f检验值都很高。在这种情况下，我可以考虑f检验值来得出结论吗？
如果是，那么F检验要考虑的显著性值是多少？
短暂性脑缺血发作
2条答案
按热度按时间kr98yfug1#
从eg.1的几个滞后来看，p值低于0.05，所以我能说y_x格兰杰导致y_y吗？
根据您的问题，我假设您要将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，表示过去1的值y_y的（滞后1）（第二列）对y_x的电流值无统计学显著影响对于number of lags (no zero) 3，当p值显示为p=0.0001时，这意味着y_y（第二列）的过去3个值（联合）对y_x（第一列）的当前值具有统计学显著影响。由方程2可知，所有的p值都是0.0000，所以y_y Granger导致y_x？
类似于上述回答，在所有情况下，对于实施例2，p值〈0.05。这意味着y_x过去值（第二列）对y_y的当前值（第一列）具有统计学上显著的影响。
所以因果关系是双向的
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，您似乎最有可能根据y_x预测y_y的值，而不是相反。如果两个输入信号都是周期性相似的循环信号，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检验值在这里起作用吗？在eg.1中，所有的f检验值都很低，而eg.2中，所有的f检验值都很高。在这种情况下，我可以考虑F检验值来得出结论吗？如果可以，那么F检验要考虑的显著性值是什么？
基于自由度，F值和p值相互关联，因为您使用p值阈值意味着您设置F值阈值。
参考文献：
1.原始码
huus2vyu2#
格兰杰因果检验是一种假设检验，
H0：其他时间序列不影响我们关注的时间序列
H1：H0为假。
如果X和Y是两个时间序列，我们想知道X是否影响Y，那么，
H0：X不是格兰杰原因Y
H1：X格兰杰导致Y，**如果p值〉0.05，则接受H0。**即X不会导致Y。
检验包括评价不同分布下的p值。
**基于SSR的F检验：**在这种情况下，统计量在零假设下具有F分布。
**基于SSR的卡方检验：**本检验的目的是确定观测数据和预期数据之间的差异是由于偶然性，还是由于您正在研究的变量之间的关系。基于卡方分布。
**似然比检验：**基本上是检验结果正确的概率与检验结果不正确的概率之比。
**参数F检验：**可用于推断总体中的两个变量是否相关。F值是两个方差的比值，或从技术上讲，是两个均方的比值。F检验称为参数检验，因为F检验中存在参数。F检验中的这些参数是均值和方差。