Bayesian Model Selection Among Dispersed Integer-Valued Time Series Models

This research evaluates model selection within a class of integer-valued time series models that feature overdispersion and extends these models to their generalized forms. The newly introduced models include: (1) dispersed integer-valued GARCH models incorporating negative binomial, double Poisson, or generalized Poisson distributions, and (2) a Double Log-form integer-valued GARCH model. The latter model avoids over-restrictions in the parameter space. We estimate parameters and select models within the Bayesian framework using adaptive Markov chain Monte Carlo (MCMC) sampling schemes, and employ the deviance information criterion (DIC) for model selection. We also design simulation studies to examine estimation accuracy and potential model misspecification. Using monthly crime counts in Bankstown, New South Wales, Australia, for an empirical illustration, our findings highlight the ability to select the most promising models among the competing ones based on DIC.