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

TL;DR

This paper investigates the asymptotic properties of residual autocorrelations in periodic vector autoregressive models with dependent errors, proposing modified tests that perform well under various dependence structures.

Contribution

It introduces new asymptotic results and test statistics for weak PVAR models with dependent innovations, improving diagnostic checking accuracy.

Findings

Proposed test statistics have good finite sample performance.

Standard tests are unreliable with dependent innovations.

New tests maintain appropriate levels under dependence.

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 nonreliable, overrejecting, or underrejecting severely, while the proposed test statistics offer satisfactory levels. An illustrative application on real data is also proposed.