Abstract

We introduce a new class of multivariate integer-valued autoregressive (INAR) models based on the notion of a common random environment. Dependence among the components of the multivariate time series is induced via a common random environment that follows a Markovian evolution. The proposed framework provides us with a dynamic multivariate generalization of the univariate INAR processes. We develop a Markov chain Monte Carlo method as well as a particle learning algorithm for Bayesian inference. We consider extensions of the model and illustrate the proposed class of models using actual multivariate time-series of counts and discuss their predictive performance.