The first-order seasonal integer-valued autoregression process with zero-inflated Poisson innovations; application to integer-valued seasonal data analysis with overdispersion

The first order Poisson integer-valued autoregressive (INAR(1)s) process with a seasonal structure has been used to model the seasonal integer-valued time series. This model, however, may not be suitable for count data with both seasonal structure and overdispersion. This paper introduces the first order seasonal integer-valued autoregressive process with zero-inflated Poisson innovations that can be used to model the seasonal integer-valued time-series with overdispersion. We discuss several probabilistic and statistical properties including stationarity of the process as well as a conditional least squares estimator and a maximum likelihood estimator of the process. Also, throughout our simulations, the applicability of these estimators to finite samples is evaluated and compared. Finally, we illustrate the usefulness of the proposed model by comparing our analysis results with ones by other competitive models considered in previous works on three real data sets.