Functional Form Of The Generalized Poisson Integer-valued GARCH Model

Overdispersion are commonly observed in time series of counts. Many authors have studies this phenomenon well. But underdispersion, the op-posite phenomenon, may also be observed in real-world and receives little attention. The integer-valued GARCH model is very popular in time series of counts. Poisson integer-valued GARCH model, negative binomial integer-valued GARCH model and generalized Poisson integer-valued GARCH model have been proposed. The former two models can only modeling overdispersion. The generalized Poisson integer-valued GARCH models can deal with not only overdispersion but also underdispersion.The Poisson distribution is popularly applied in time series of counts and its generalized form is well studied. Based on Poisson integer-valued GARCH model, we develop a functional form of generalized Poisson integer-valued GARCH model, which provides a tool for modeling overdispersion and un-derdispersion. We analyze the mean and variance of the model and drive the autocorrelation structure. Then we discuss the maximum likelihood estima-tors for the parameters. We apply the inverse transform method to generating discrete random variables and do some simulations. Simulations indicates that the model can cope with overdispersion as well as underdispersion. We apply the model to a series of random variables. The results show that it performs better than other models in the literature.