An Integer GARCH model for a Poisson process with time varying zero-inflation

TL;DR

This paper introduces a novel integer GARCH model for zero-inflated Poisson processes with time-varying zero-inflation, improving fit over traditional models through EM and MLE estimation methods.

Contribution

It extends existing zero-inflated INGARCH models by allowing the zero-inflation parameter to vary over time, enhancing modeling flexibility and accuracy.

Findings

Both EM and MLE methods yield good parameter estimates.

The proposed model outperforms traditional zero-inflated INGARCH in real data applications.

Simulation results confirm the effectiveness of the estimation procedures.

Abstract

A time-varying zero-inflated serially dependent Poisson process is proposed. The model assumes that the intensity of the Poisson Process evolves according to a generalized autoregressive conditional heteroscedastic (GARCH) formulation. The proposed model is a generalization of the zero-inflated Poisson Integer GARCH model proposed by Fukang Zhu in 2012, which in return is a generalization of the Integer GARCH (INGARCH) model introduced by Ferland, Latour, and Oraichi in 2006. The proposed model builds on previous work by allowing the zero-inflation parameter to vary over time, governed by a deterministic function or by an exogenous variable. Both the Expectation Maximization (EM) and the Maximum Likelihood Estimation (MLE) approaches are presented as possible estimation methods. A simulation study shows that both parameter estimation methods provide good estimates. Applications to two real-life data sets show that the proposed INGARCH model provides a better fit than the traditional zero-inflated INGARCH model in the cases considered.