A New Approach to Integer-Valued Time Series Modeling: The Neyman Type-A INGARCH Model*

Abstract

The aim of this paper is to develop a probabilistic study of a wide class of conditionally heteroscedastic models recently introduced in the literature, the compound Poisson INGARCH processes [7]. This class includes, in particular, some well-known models like the Poisson INGARCH of Ferland, Latour, and Oraichi [4] or the negative binomial and generalized Poisson INGARCH introduced by Zhu in 2011 and 2012, respectively. Within this class, we analyze the existence and ergodicity of a strictly and weakly stationary solution. For a new particular model of that class, the Neyman type-A INGARCH model, we derive the autocorrelation function, analyze the existence of higher-order moments, and obtain an explicit form of their first four cumulants, from which we deduce the corresponding skewness and kurtosis.