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Asymptotic inference for nearly unstable INAR(1) models

Part of: Parametric inference Markov processes Inference from stochastic processes

Published online by Cambridge University Press:  14 July 2016

M. Ispány ,
G. Pap  and
M. C. A. van Zuijlen
M. Ispány*
Affiliation:
University of Debrecen
G. Pap*
Affiliation:
University of Debrecen
M. C. A. van Zuijlen*
Affiliation:
University of Nijmegen
*
∗Postal address: Institute of Mathematics and Informatics, University of Debrecen, Pf. 12, H-4010 Debrecen, Hungary
∗Postal address: Institute of Mathematics and Informatics, University of Debrecen, Pf. 12, H-4010 Debrecen, Hungary
∗Postal address: Department of Mathematics, University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands. Email address: [email protected]
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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 n3/2. Nearly critical Galton–Watson processes with unobservable immigration are also discussed.

Keywords

Discrete-time seriesINAR(1) modelstable and nearly unstable modelsconditional least-squares estimatorasymptotic distributionGalton–Watson process

MSC classification

Primary: 62F12: Asymptotic properties of estimators
Secondary: 62M10: Time series, auto-correlation, regression, etc. 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 3 , September 2003 , pp. 750 - 765
Copyright
Copyright © Applied Probability Trust 2003 

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