Asymptotic inference for moderate deviations from a unit root of nearly unstable INAR(1) processes

Abstract

ABSTRACT The INAR(1) processes with coefficients , where c>0 is a fixed constant and is a deterministic sequence growing to infinity at a slower rate than n, which are often referred to as nearly unstable INAR processes with moderate deviations from a unit root. We consider some basic properties of the processes and obtain the conditional least squares estimation of the coefficient , which converges to a normal distribution at speed . The simulation study provides numerical support for the theoretical results. The practical utility is illustrated in the data sets about liquor offences, claims of short-term disability and COVID-19, respectively.