Integer Valued AR Processes with Explanatory Variables

Abstract

Integer valued AR (INAR) processes are perfectly suited for modelling count data. We consider the inclusion of explanatory variables into the INAR model to extend the applicability of INAR models and give an alternative to Poisson regression models. An efficient MCMC algorithm is constructed to analyze the model and incorporates both explanatory variable and order selection. The methodology is illustrated by analyzing monthly polio incidences in the USA 1970-1983 and claims from the logging industry to the British Columbia Workers ’ Compensation Board 1985-1994