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Recently, there has been a growing interest in integer-valued volatility models. In this paper, using a martingale transformation, a general theorem on moment properties of a class of integer-valued volatility models is given with simpler proof. We show that the first two moments obtained in the recent literature are special cases. In addition, we also derive the closed form expressions of the kurtosis and skewness formula for the models. The results are very useful in understanding the behaviour of the process and in estimating the parameters of the models using quadratic estimating functions method. Specifically, we derive the optimal function of INGARCH(1,1) and obtain the estimated parameters of interest via simulation. We show that the performance of the quadratic estimating functions method is superior compared to maximum likelihood and least square methods. For illustration, we fit the INGARCH(1,1) on 108 monthly strike data from January 1994 to December 2002 from Jung et al. (2005).

Moment Properties And Quadratic Estimating Functions For Integer-Valued Time Series Models