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I have a VAR(1) model with 10 variables. I want to check what is Granger causality and examine impulse response function. Let's say that I have equation for variable Y, X is a Granger cause for Y, Z and other variables are not a Granger cause for Y. Can I test the impulse response function only for the variables which are Granger cause? I mean, do I have to check the IRF only for X?

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Can I test the impulse response function only for the variables which are Granger cause? I mean, do I have to check the IRF only for X?

You can always check the IRF for all variables but the Granger causality is an indicator of the soundness that the IRF might have. For example, an bad performing IRF could have positive and negative confidence intervals, or a cyclical behaviour.

However another key factor is lag length. You need to optimize the lag length in order to obtain better results. Sometimes the test statistics and/or the information criteria (AIC, BIC) are not exactly pointing to an specific length and you might need to choose quite arbitrarily.

Depending on the software, there are subtypes of Granger causality test, basically pairwise and GroupWise. The latter is more important in VAR Models. If none of the equations present Granger Causality, perhaps you may have to reduce the size of the VAR to only Y and X.

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    $\begingroup$ AIC and BIC are not test statistics; these are information criteria. Also, consider reformulating equations granger cause. $\endgroup$ May 14 at 14:32

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