The asymptotic structure of nearly unstable non-negative integer-valued AR(1) models

TL;DR

This paper investigates the asymptotic behavior of nearly unstable non-negative integer-valued AR(1) models, revealing a Poissonian limit experiment and discussing efficient estimation and testing procedures.

Contribution

It provides the first detailed analysis of the local asymptotic structure for nearly unstable non-negative integer-valued AR(1) processes, highlighting the Poissonian nature of the limit experiment.

Findings

Limit experiment is Poissonian.

Efficient estimation of the autoregression parameter is discussed.

Efficient testing for a unit root is analyzed.

Abstract

This paper considers non-negative integer-valued autoregressive processes where the autoregression parameter is close to unity. We consider the asymptotics of this `near unit root' situation. The local asymptotic structure of the likelihood ratios of the model is obtained, showing that the limit experiment is Poissonian. To illustrate the statistical consequences we discuss efficient estimation of the autoregression parameter and efficient testing for a unit root.