Diagnostic checking of periodic vector autoregressive time series models with dependent errors

Abstract

In this article, we study the asymptotic behaviour of the residual autocorrelations for periodic vector autoregressive time series models (PVAR henceforth) with uncorrelated but dependent innovations (i.e., weak PVAR). We then deduce the asymptotic distribution of the Ljung–Box-McLeod modified Portmanteau statistics for weak PVAR models. In Monte Carlo experiments, we illustrate that the proposed test statistics have reasonable finite sample performance. When the innovations exhibit conditional heteroscedasticity or other forms of dependence, it appears that the standard test statistics (under independent and identically distributed innovations) are generally unreliable, overrejecting, or underrejecting severely, while the proposed test statistics offer satisfactory levels. The proposed methodology is employed in the analysis of two river flows.