On the distribution of the residual cross-correlations of infinite order vector autoregressive series and applications

Here we derive the asymptotic distribution of an arbitrary vector of residual cross-correlations resulting from the fitting of finite autoregressions to two uncorrelated infinite order vector autoregressive series. Its asymptotic distribution is the same multivariate normal as the one of the corresponding vector of cross-correlations between the two innovation series. The application of that result for testing the uncorrelatedness of two series is also discussed.