多元格兰杰因果关系 [英] Multivariate Granger's causality

问题描述

我在进行多元Granger因果检验时遇到问题.我想检查条件第三个变量是否会影响因果检验的结果.这是一个基于我之前提出的问题的单个因变量和自变量的样本，并由@Alex

I'm having issues doing a multivariate Granger's causal test. I'll like to check if conditioning a third variable affects the results of a causal test. Here's one sample for a single dependent and independent variable based on an earlier question I asked and was answered by @Alex

格兰杰因果关系按列

library(lmtest)
M1<- matrix( c(2,3, 1, 4, 3, 3, 1,1, 5, 7), nrow=5, ncol=2)
M2<- matrix( c(7,3, 6, 9, 1, 2, 1,2, 8, 1), nrow=5, ncol=2)  
M3<- matrix( c(1, 3, 1,5, 7,3, 1, 3, 3, 4), nrow=5, ncol=2)

例如，条件线性回归方程将为

For example, the equation for a conditioned linear regression will be

formula = y ~ w + x * z

请问如何根据第三个或第四个变量进行此测试?

How do I carry out this test as a function of a third or fourth variable please?

推荐答案

1.固定变量的解决方案已经成熟:参见

1. The solution for stationary variables are well-established: See FIAR (v 0.3) package.

这是本文，与包含具体内容的软件包有关多元Granger因果关系的示例(在所有变量均为平稳的情况下).
第12页:理论，第15页:实践.

This is the paper related with the package that includes concrete example of multivariate Granger causality (in the case of all of the variables are stationary).
Page 12: Theory, Page 15: Practice.

2..对于混合(固定，非固定)变量，请首先使所有变量保持平稳(通过差分等).不要处理固定的(已经固定的).现在，再次完成上述过程(以防万一).

2. In case of mixed (stationary, nonstationary) variables, make all the variables stationary first (via differencing etc.). Do not handle stationary ones (they are already stationary). Now again, you finish by the above procedure (in case I).

3..如果是非综合非平稳"变量，则不需要VECM.使用固定变量运行VAR(当然，首先使它们固定).应用 FIAR :: condGranger 等

3. In case of "non-cointegrated nonstationary" variables, then there is no need for VECM. Run VAR with the stationary variables (by making them stationary first, of course). Apply FIAR::condGranger etc.

4.对于协整非平稳"变量，答案的确很长:Johansen过程(通过 urca :: cajo 检测排名)应用 vec2var 将VECM转换为VAR(因为 FIAR 基于VAR).约翰·亨特(John Hunter)的最新书很好地总结了在最后一种情况下可能发生的事情以及可以做什么

4. In case of "cointegrated nonstationary" variables, the answer is really really very long: Johansen Procedure (detect rank via urca::cajo) Apply vec2var to convert VECM to VAR (since FIAR is based on VAR). John Hunter's latest book nicely summarizes what can happen and what can be done in this last case.

您可能还想阅读此.

据我所知:通过通过VAR进行块外生性Wald检验"，条件/部分Granger因果关系取代了GC.

To my knowledge: Conditional/partial Granger causality supersides the GC via "Block exogeneity Wald test over VAR".

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