Granger Causality Test in PROC VARMAX with Three Variables

tugasakhir — Mon, 25 May 2026 06:49:20 GMT

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.

topic Granger Causality Test in PROC VARMAX with Three Variables in SAS Forecasting and Econometrics

Granger Causality Test in PROC VARMAX with Three Variables