A new bivariate integer-valued autoregressive model with interaction effect

In this paper, we propose a new bivariate integer-valued autoregressive process with interaction effects, referred to as the IEBINAR(1) model. We consider three estimation methods for the unknown parameters of interest: conditional least squares, conditional maximum likelihood, and a two-step estimation approach. The asymptotic properties of the estimators are established. The performance of these estimation methods is compared through simulation experiments. Furthermore, we conduct hypothesis testing to examine the existence of interaction effects in the IEBINAR(1) model. Finally, a real data application is presented to evaluate the performance of the proposed model.