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 models. The proposed specification encompasses a wide range of conditional distributions of counts. We study its probabilistic structure and design Markov chain Monte Carlo 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 using marginal likelihoods and forecast evaluation using point and density forecasts are also considered.