Observation driven models for Poisson counts

This paper is concerned with a general class of observation driven models for time series of counts whose conditional distributions given past observations and explanatory variables follow a Poisson distribution. These models provide a flexible framework for modeling a wide range of dependence structures. Conditions for stationarity and ergodicity of these processes are established from which the large sample properties of the maximum likelihood estimators can be derived. Simulations are provided to give additional insight into the finite sample behavior of the estimates. Finally an application to a regression model for daily counts of accident and emergency room presentations for asthma at several Sydney hospitals is described.