On an integer-valued stochastic intensity model for time series of counts

We propose a broad class of count time series models, the mixed Poisson integer-valued stochastic intensity (INSI) models. The proposed parameter- driven specification in which the log-intensity follows a drifted autoregression encompasses a wide range of conditional distributions of counts. We study its probabilistic structure and design Markov chain Monte Carlo estimation algorithms for two cases; the Poisson and the negative binomial distributions. The methodology is applied to simulated data as well as to various data sets. Model comparison is conducted using marginal likelihoods and forecast evaluation using point and density forecasts. The INSI specifications were also compared against the Poisson and negative binomial integer-valued GARCH (INGARCH) models, within the Bayesian framework, where the former dominated the latter.