A statistical study for some classes of first-order mixed generalized binomial autoregressive models

In order to solve the modeling problems of integer-valued time series with complex and dependent structures, this article proposes some classes of first-order mixed generalized binomial autoregressive models. Basic probabilistic and statistical properties of the models are discussed. The parameters of models are estimated by the conditional maximum likelihood method. Also, the asymptotic properties and the numerical results of these estimators are obtained. Finally, the good performances of these models are illustrated, among other competitive models in the literature, by an application to the data of weekly rainy days.