A negative binomial mixture integer-valued GARCH model

Abstract

This paper generalizes the negative binomial integer-valued GARCH model (NBINGARCH) to a negative binomial mixture integer-valued GARCH (NBMINGARCH) for modeling time series of counts with presence of overdispersion. This class of models consists of a mixture of K stationary or non-stationary negative binomial integer-valued GARCH components. The advantage of these models over the NBINGARCH models includes the ability to handle multimodality and nonstationary components. Compared to the MINGARCH models, this class of models is more flexible to describe the greater degrees of overdispersion. The necessary and sufficient first and second order stationarity conditions are investigated. The estimation of parameters is done through an EM algorithm and the model is selected by some information criterions. Some simulation results and real data application are provided. Keywords: Time series of counts, Mixture model, Negative binomial, Overdispersion. AMS 2010 Mathematics Subject Classification : 62F10, 62M10