Bartlett correction in stationary VARs

We derive the Bartlett correction for a simple hypothesis on the regression parameters
in a multivariate stationary autoregressive process. Three applications illustrate the use of the correction: the test for absence of autocorrelation of any order, a simple hypothesis on the autoregressive parameters and two tests for weak exogeneity in the cointegrated VAR model. In the first of these tests, the cointegration space is known, in the second it is not. The Bartlett correction performs well in all simulation studies, except in the one of the last test, that is a test for weak exogeneity in the cointegrated VAR with an unknown cointegration space.