The Multivariate Ginar(p) Process

Abstract

A criterion is given for the existence of a stationary and causal multivariate integer-valued autoregressive process, MGINAR( p ). The autocovariance function of this process being identical to the autocovariance function of a standard Gaussian MAR( p ), we deduce that the MGINAR( p ) process is nothing but a MAR( p ) process. Consequently, the spectral density is directly found and gives good insight into the stochastic structure of a MGINAR( p ). The estimation of parameters of the model, as well as the forecasting of the series, is discussed.