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

Yacouba Boubacar Maïnassara and Eugen Ursu

Journal of Multivariate Analysis, 2025, vol. 205, issue C

Abstract: In this article, we study the asymptotic behavior 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.

Keywords: Diagnostic checking; Portmanteau tests; Residual autocorrelation; Weak periodic VAR (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.jmva.2024.105379

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