Causality conditions and autocovariance calculations in PVAR models

Abstract

This paper studies the causality conditions and autocovariance calculations in periodic vector auto-regressions. A state-space representation is exploited to extract a simple, necessary and sufficient condition for periodic stationarity, under which the autocovariances can be expressed in a simple but tractable form. The proposed methods compute the autocovariances for distinct seasons separately, thereby facilitating efficient computation for models with a large period.