On suitability of negative binomial marginals and geometric counting sequence in some applications of Combined INAR(p) model

Abstract

A combined negative binomial integer-valued autoregressive process of order $p$ is defined. Correlation structure and regression properties are presented. Model parameters are estimated using conditional least squares and Yule-Walker methods and the asymptotic distributions of the obtained estimators are derived. Model interpretation is provided, especially focusing on usage of geometric counting sequence and negative binomial marginals and further it is justified by application of the introduced model to certain counting data, where it is compared with some other possible known model solutions.