Estimation Methods for a Flexible INAR(1) COM-Poisson Time Series Model

Time series of counts occur in many real-life situations where they exhibit various forms of dispersion. To facilitate the modeling of such time series, this paper introduces a flexible first-order integer-valued non-stationary autoregressive (INAR(1)) process where the innovation terms follow a Conway-Maxwell Poisson distribution (COM-Poisson). To estimate the unknown parameters in this model, different estimation approaches based on likelihood and quasi-likelihood formulations are considered. From simulation experiments and a real-life data application, the Generalized Quasi-Likelihood (GQL) approach yields estimates with lower bias than the other estimation approaches.