INAR approximation of bivariate linear birth and death process

Abstract In this paper, we propose a new type of univariate and bivariate Integer-valued autoregressive model order one (INAR(1)) to approximate linear birth death process with constant rates. Under specific parametric setting, the dynamic transition probabilities probability generating function INAR(1) will converge that as length subintervals goes 0. Due simplicity Markov structure, maximum likelihood estimation is feasible for model, which not case multivariate process. This means statistical inference can be achieved via model.