A new class of integer-valued GARCH models for time series of bounded counts with extra-binomial variation

This article considers a modeling problem of integer-valued time series of bounded counts in which the binomial index of dispersion of the observations is greater than one, i.e., the observations inhere the characteristic of extra-binomial variation. Most methods analyzing such characteristic are based on the conditional mean process instead of the observed process itself. To fill this gap, we introduce a new class of beta-binomial integer-valued GARCH models, establish the geometric moment contracting property of its conditional mean process, discuss the stationarity and ergodicity of the observed process and its conditional mean process, and give some stochastic properties of them. We consider the conditional maximum likelihood estimates and establish the asymptotic properties of the estimators. The performances of these estimators are compared via simulation studies. Finally, we apply the proposed models to two real data sets.