A geometric bivariate time series with different marginal parameters

A new bivariate non-negative integer-valued autoregressive model of order one is introduced. The model is based on the binomial thinning operator. The univariate processes that compose the model are geometrically distributed with not necessarily equal mean parameters. Some properties of the model are derived and discussed. The unknown parameters are estimated and some of their asymptotic properties are derived and discussed. The model performance is tested on real data.