A goodness-of-fit test for VARMA(p, q) models

A goodness-of-fit approach for multivariate VARMA(p, q) models is presented. The idea is to consider a stochastic process based on a modified residual correlation matrix sequence, that is shown to converge to the Brownian bridge. Standard criteria based on this new random function, as for instance the Kolmogorov-Smirnov and Cramér-von Mises statistics, will have then a pivotal null asymptotic distribution. The properties of these two methods are investigated by simulation. As compared with the traditional methods in this area, their size does not depend critically on the choice of any lag parameter value, and they have better power properties.