Generalized Poisson autoregressive models for time series of counts

To better describe the characteristics of time series of counts such as over-dispersion, asymmetry, structural change, and a large proportion of zeros, this paper considers a class of generalized Poisson autoregressive models that properly capture flexible asymmetric and nonlinear responses through a switching mechanism. We also investigate zero-inflated generalized Poisson autoregressive models with a structural break that can cope with data having a large portion of zeros and changes in dynamics. We employ an adaptive Markov Chain Monte Carlo (MCMC) sampling scheme to locate the structural break and to estimate model parameters. As an illustration, we conduct a simulation study and empirical analysis of New South Wales crime data sets. Our findings show a remarkable improvement by modeling the data based on such generalized Poisson autoregressive models and the Bayesian method.