On the asymptotic distribution of residual autocovariances in VARX models with applications

Abstract

In this paper, we derive the asymptotic distribution of residual autocovariance matrices in the class of vector autoregressive models with explanatory variables (VARX). The asymptotic distribution of residual autocorrelation matrices is also obtained. New test statistics are proposed as an application of our main result. Test statistics at individual lags and portmanteau statistics are introduced and their asymptotic distributions are established. The proposed test, statistics are illustrated in a small simulation study.