On random coefficient INAR(1) processes

TL;DR

This paper investigates the asymptotic properties of random coefficient INAR(1) processes, focusing on extreme value limits and partial sum growth when the additive component follows a stable law domain of attraction.

Contribution

It provides new insights into the asymptotic behavior of the process under stable law conditions, extending previous models.

Findings

Weak limits of extreme values characterized

Growth rate of partial sums analyzed

Conditions for stable law domain of attraction established

Abstract

The random coefficient integer-valued autoregressive process was introduced by Zheng, Basawa, and Datta. In this paper we study the asymptotic behavior of this model (in particular, weak limits of extreme values and the growth rate of partial sums) in the case where the additive term in the underlying random linear recursion belongs to the domain of attraction of a stable law.