Inferences for integer-valued time series models / Nurul Najihah Mohamad - Nurul Najihah, Mohamad (2017)
Recently there has been a growing interest in integer-valued volatility models. The need for such time series models arises in different areas including biomedicine, insur- ance and finance. Here, we look at a class of integer-valued GARCH time series models which are of interest to the practitioners. The models are assuming the form of GARCH model such that the conditional distribution of the process follows one of the following distributions; Poisson, negative binomial and zero-inflated Poisson. In this study, a general theorem on the moment properties of the class of integer-valued volatility models is derived using martingale transformation with much simpler proofs. We show the first two moments obtained in the recent literature as special cases. In addition, we derive the closed form expressions of the kurtosis and skewness formula for these three models. The results are very useful in understanding the behaviour of the processes. We then estimate the parameters of the class of integer-valued volatility models via the quadratic estimating functions theory. Specifically, the optimal estimating functions for each process are derived. Through a finite sample size investigation, we compare the performance of the quadratic estimating functions (QEF) method with the maximum likelihood and estimating functions (EF) methods. We show that the quadratic estimating functions method performs better in terms of unbiasness and mean square error. For illustration, we fit the models on real data sets.