First‐order Integer‐valued Autoregressive (Inar(1)) Process

Abstract. A simple model for a stationary sequence of integer‐valued random variables with lag‐one dependence is given and is referred to as the integer‐valued autoregressive of order one (INAR(1)) process. The model is suitable for counting processes in which an element of the process at time t can be either the survival of an element of the process at time t ‐ 1 or the outcome of an innovation process. The correlation structure and the distributional properties of the INAR(1) model are similar to those of the continuous‐valued AR(1) process. Several methods for estimating the parameters of the model are discussed, and the results of a simulation study for these estimation methods are presented.