A mixed generalized Poisson INAR model with applications

A very attractive property of the mixed integer-valued autoregressive model is that it can capture structural changes. Inspired by this, we propose a mixed generalized Poisson integer-valued autoregressive model with a mixture of the quasi-binomial and generalized Poisson thinning operators. The first-order and higher-order mixed models are introduced, respectively. Some properties of the mixed models are presented. Conditional maximum likelihood estimation is considered for the parameters of the proposed model. The mean, median and mode of the conditional distribution are used to predict the one-step-ahead values. Furthermore, an approximate Bayesian model averaging prediction with the Bayesian information criterion is introduced to the higher-order models in the application to real data. Some Monte Carlo simulation results are presented for assessing the performance of parameter estimation and forecasting methods. At last, the applications of proposed models to real data are given for illustrating purposes.