Zero Inflated Poisson Xgamma INAR(1) Model and Its Applications

Abstract

The first order non-negative integer valued autoregressive process is widely used for counts of events over time. It is obvious that if the innovations are Poisson distributed, then the marginal model is Poisson. However, this marginal process may not hold for the overdispersed count data. An example of one common type of overdispersion is when zero counts are more likely than claimed by the Poisson marginal model. In this regard, we introduce a zero inflated version of a discrete compound model and developed its first integer autoregressive process using zero inflated Poisson Xgamma (ZIPXG) innovations. We derive different structural properties of the INAR(1) model and estimated the parameters by conditional maximum likelihood, Yule-Walker and Bayesian methods. Further a simulation study has been performed to investigate the behavior of these estimated parameters. To illustrate the utility of the newly proposed INAR(1) model, a time series data on submissions to animal health laboratories has been analyzed.