Periodic negative binomial INGARCH(1, 1) model

Abstract

In this paper, we introduce a class of periodic negative binomial integer-valued generalized autoregressive conditional heteroskedastic model. The basic probabilistic and statistical properties of this class are studied. Indeed, the first and the second moment periodically stationary conditions are established. The closed-forms of these moments are, under the obtained conditions, derived. Furthermore, the condition for the existence of higher moment orders and their explicit formula in terms of the parameters are established. The periodic autocovariance structure is also considered while providing the closed-form of the periodic autocorrelation function. The Yule-Walker (YW), the conditional least squares (CLS), and the conditional maximum likelihood (CML) methods are applied to estimate the underlying parameters. The performances of these methods are compared through a simulation study. An application to a real data set is provided.