Bivariate first-order random coefficient integer-valued autoregressive processes

In this paper, we propose a new bivariate first-order random coefficient integer-valued autoregressive (BRCINAR(1)) process with dependent innovations. Some basic probabilistic and statistical properties of this model are obtained. Estimators of unknown parameters are derived by using Yule–Walker, conditional least squares and conditional maximum likelihood methods. The asymptotic properties of the estimators are established. The performance of these estimators is compared through a simulation experiment. Moreover, the coherent forecasting for BRCINAR(1) model is addressed. Finally, an application to a real data example is investigated to assess the performance of the model.