Bivariate zero truncated Poisson INAR(1) process

In this paper, we propose a new stationary bivariate first order integer-valued autoregressive (BINAR(1)) process with zero truncated Poisson marginal distribution. Some properties about this process are considered, such as probability generating function, autocorrelations, expectations and covariance matrix under conditional and unconditional situation. We also establish the strict stationarity and ergodicity of the process. Estimators of unknown parameters are derived by using Yule–Walker, conditional least squares and maximum likelihood methods. The performance of the proposed estimation procedures are evaluated through Monte Carlo simulations. An application to a real data example is also provided.