Random coefficient bivariate INAR(1) process

A bivariate autoregressive model for time series of counts is presented. The model is composed of survival and innovation components. The dependence between series is achieved through innovation parts. Autoregression is modelled with the survival component which is based on binomial thinning operator. Coefficients that figures here are random variables. Statistical properties of the model are presented. Existence, stationarity and ergodicity of the model is proved. We focus on the model where innovation components follow bivariate Poisson distribution. We suggest Conditional maximum likelihood and Method of moments for parameter estimation. Both methods are tested on simulated data sets.