Asymptotic inference for nearly unstable INAR(1) models

Ispány, Márton and Pap, Gyula and van Zuijlen, M. C. A. (2003) Asymptotic inference for nearly unstable INAR(1) models. Journal of Applied Probability, 40 (3). pp. 750-765. ISSN 0021-9002

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Abstract

A sequence of first-order integer-valued autoregressive (INAR(1)) processes is investigated, where the autoregressive-type coefficient converges to 1. It is shown that the limiting distribution of the conditional least squares estimator for this coefficient is normal and the rate of convergence is n(3/2). Nearly critical Galton-Watson processes with unobservable immigration are also discussed.

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