FIRST‐ORDER INTEGER‐VALUED AUTOREGRESSIVE (INAR(1)) PROCESS

TLDR

The integer‑valued autoregressive of order one (INAR(1)) process is a simple stationary model for integer‑valued random variables with lag‑one dependence, whose correlation structure and distributional properties resemble those of the continuous‑valued AR(1) process. The INAR(1) model describes counting processes where each observation is either the survival of a previous element or the outcome of an innovation process. Several parameter‑estimation methods are discussed, and a simulation study evaluates their performance. This abstract summarizes the INAR(1) process.

Abstract

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.