  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.
