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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

Granger's causality test by column

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)

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

formula = y ~ w + x * z

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

Sotos
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Joke O.
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1 Answers1

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

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. 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. 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. 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.

You may wanna read this as well.

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

Erdogan CEVHER
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