“…Hill (
2007) develops a long‐run Granger causality test for a trivariate VAR process
, where the causality of interest is basically investigated with full model information and the proposed test strategy is restricted on the case that
includes merely one variable (i.e., a univariate set). Al‐Sadoon (
2014,
2019) discusses the estimation and testing of subspace Granger causality from
to
, where
and
are both multivariate time series in vector form. The idea is that Granger causality can be limited to subspaces of
and
, say,
may not help on predicting co‐movements of
in all directions, and, not all directions for the co‐movements of
can help predict
.…”