In general, Wald tests for the Granger non-causality in vector autoregressive (VAR) process are known to have non-standard asymptotic properties for cointegrated systems. However, that may have standard asymptotic properties depending on the rank of the submatrix of cointegration. In this paper,...

The usual Wald test for the Granger non-causality in cointegrated vector autoregressive (VAR) processes is known to have the asymptotically non-standard distribution. There have been proposed a few alternative (inefficient) methods which give the asymptotically standard distribution. However,...