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,...

In this paper, we propose a new approach to test the hypothesis of long-run Granger non-causality in cointegrated systems. We circumvent the problem of singularity of the variance-covariance matrix associated with the usual Wald type test by proposing a generalized inverse procedure, and an...

In this paper, we propose a new approach to test the hypothesis of long-run Granger non-causality in cointegrated systems. We circumvent the problem of singularity of the variance-covariance matrix associated with the usual Wald type test by proposing a generalized inverse procedure, and an...

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,...