A mixture integer-valued ARCH model

We propose a mixture integer-valued ARCH model for modeling integer-valued time series with overdispersion. The model consists of a mixture of K stationary or non-stationary integer-valued ARCH components. The advantages of the mixture model over the single-component model include the ability to handle multimodality and non-stationary components. The necessary and sufficient first- and second-order stationarity conditions, the necessary arbitrary-order stationarity conditions, and the autocorrelation function are derived. The estimation of parameters is done through an EM algorithm, and the model is selected by three information criterions, whose performances are studied via simulations. Finally, the model is applied to a real dataset.