Local Asymptotic Normality and Efficient Estimation for INAR(p) Models

Abstract

Integer‐valued autoregressive (INAR) processes have been introduced to model non‐negative integer‐valued phenomena that evolve in time. The distribution of an INAR(p) process is determined by two parameters: a vector of survival probabilities and a probability distribution on the non‐negative integers, called an immigration distribution. This paper provides an efficient estimator of the parameters, and in particular, shows that the INAR(p) model has the Local Asymptotic Normality property.