Count Time Series Models

We review regression models for count time series. We discuss the approach which is based on generalized linear models and the class of integer autoregressive processes. The generalized linear models framework provides convenient tools for implementing model fitting and prediction using standard software. Furthermore, this approach provides a natural extension to the traditional ARMA methodology. Several models have been developed along these lines, but conditions for stationarity and valid asymptotic inference were given in the literature only recently. We review several of these facts. In addition, we consider integer autoregressive models for count time series and discuss estimation and possible extensions based on real data applications.