Diagnostic checking for partially nonstationary multivariate ARMA models

Abstract

This paper studies the residual autocorrelation functions (ACFs) of partially nonstationary multivariate autoregressive moving-average (ARMA) models. The limiting distributions of the full rank estimators and the Gaussian reduced rank estimators are derived. Using these results, we derive the limiting distributions of the residual ACFs under full rank and reduce rank estimations. Based on these limiting distributions, we construct the portmanteau statistics for model checking. It is shown that these statistics asymptotically follow χ2-distributions. Simulations are carried out to assess their performances in finite samples and two real examples are given.