Suppose there are three variables, say (x), (y), and (z), and they are modeled using a VARMA model in PROC VARMAX.
For the Granger causality test, I would like to ask about the correct way to specify and interpret the test in a multivariate setting. In many examples, Granger causality is usually explained pairwise, for example whether (x) Granger-causes (y), or whether (y) Granger-causes (x).
However, if the VARMA model includes three endogenous variables, should the Granger causality test be conducted only between two variables at a time, for example:
(x --> y),
(y --> x),
(x --> z),
(z --> x),
- (y --> z),
- (z --> y)
or should it be tested in a conditional or joint sense, for example:
whether (x) Granger-causes (y) while controlling for (z),
whether (x) Granger-causes (z) while controlling for (y),
or whether (y) and (z) jointly Granger-cause (x)?
In other words, when using PROC VARMAX with three endogenous variables, should the Granger causality test be interpreted as a pairwise relationship between two variables, or as a test within the full multivariate system?
Any explanation or guidance on how to correctly conduct and interpret this Granger causality test in PROC VARMAX would be greatly appreciated.
Thank you.
