A MIXTURE INTEGER-VALUED GARCH MODEL

In this paper, we generalize the mixture integer-valued ARCH model (MINARCH) introduced by Zhu et al. (2010) (F. Zhu, Q. Li, D. Wang. A mixture integer-valued ARCH model, J. Statist. Plann. Inference, 140 (2010), 2025-2036.) to a mixture integer-valued GARCH (MINGARCH) for modeling time series of counts. This model includes the ability to take into account the moving average (MA) components of the series. We give the necessary and sufficient conditions for first and second order stationarity solutions. The estimation is done via the EM algorithm. The model selection problem is studied by using three information criterions. We also study the performance of the method via simulations and include a real data application.