Time-Varying Dispersion Integer-Valued GARCH Models

TL;DR

This paper introduces a novel class of time-varying dispersion INGARCH models that extend traditional models by allowing dynamic mean and dispersion parameters, with theoretical properties and practical applications demonstrated.

Contribution

It develops a new framework for INGARCH models with time-varying dispersion, including stationarity conditions, estimation methods, and a bootstrap test for dispersion dynamics.

Findings

Model effectively captures time-varying dispersion in count data.

Bootstrap test accurately detects changes in dispersion.

Application to measles data shows improved fit over traditional models.

Abstract

We propose a general class of INteger-valued Generalized AutoRegressive Conditionally Heteroscedastic (INGARCH) processes by allowing time-varying mean and dispersion parameters, which we call time-varying dispersion INGARCH (tv-DINGARCH) models. More specifically, we consider mixed Poisson INGARCH models and allow for dynamic modeling of the dispersion parameter (as well as the mean), similar to the spirit of the ordinary GARCH models. We derive conditions to obtain first and second-order stationarity, and ergodicity as well. Estimation of the parameters is addressed and their associated asymptotic properties are established as well. A restricted bootstrap procedure is proposed for testing constant dispersion against time-varying dispersion. Monte Carlo simulation studies are presented for checking point estimation, standard errors, and the performance of the restricted bootstrap approach. We apply the tv-DINGARCH process to model the weekly number of reported measles infections in North Rhine-Westphalia, Germany, from January 2001 to May 2013, and compare its performance to the ordinary INGARCH approach.