Flexible INAR(1) models for equidispersed, underdispersed or overdispersed counts

Equidispersed, underdispersed and overdispersed count data are commonly encountered in practice. To better describe these data characteristics, this paper develops two classes of INAR(1) processes, which not only can model a wide range of overdispersion and underdispersion, but also have ability to describe the zero-inflated and zero-deflated characteristics of the count data. The probabilistic and statistical properties of the two processes are studied. Estimators of the model parameters are derived by using conditional maximum likelihood (CML) and modified conditional least squares (MCLS) methods. Some asymptotic properties and numerical results of the estimators are investigated. Three real examples are given to show the flexibility and usefulness of the proposed models.