Mixing properties of non-stationary INGARCH(1,1) processes

TL;DR

This paper establishes mixing properties for a wide class of non-stationary Poisson count time series, including models with explosive trends, using coupling techniques and contraction conditions.

Contribution

It introduces verifiable conditions for absolute regularity in non-stationary Poisson count models, extending previous results to models with trends and providing practical hypothesis testing tools.

Findings

Proves geometric rate absolute regularity for non-stationary Poisson-GARCH.

Provides verifiable conditions for a broad class of models.

Demonstrates practical application in hypothesis testing.

Abstract

We derive mixing properties for a broad class of Poisson count time series satisfying a certain contraction condition. Using specific coupling techniques, we prove absolute regularity at a geometric rate not only for stationary Poisson-GARCH processes but also for models with an explosive trend. We provide easily verifiable sufficient conditions for absolute regularity for a variety of models including classical (log-)linear models. Finally, we illustrate the practical use of our results for hypothesis testing.