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arXiv · 2207.10114

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

Isuru Ratnayake·V. A. Samaranayake
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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.

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Isuru Ratnayake, V. A. Samaranayake. 2022-07-20. An Integer GARCH model for a Poisson process with time varying zero-inflation. https://doi.org/10.1371/journal.pone.0285769

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