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Random coefficients bifurcating autoregressiveprocesses

Published online by Cambridge University Press:  03 October 2014

Benoîte de Saporta ,
Anne Gégout-Petit  and
Laurence Marsalle
Benoîte de Saporta
Affiliation:
Univ. Bordeaux, Gretha, UMR 5113, IMB, UMR 5251, 33400 Talence, France CNRS, Gretha, UMR 5113, IMB, UMR 5251, 33400 Talence, France INRIA Bordeaux Sud Ouest, team CQFD, 33400 Talence, France
Anne Gégout-Petit
Affiliation:
Univ. Bordeaux, IMB, UMR 5251, 33400 Talence, France CNRS, IMB, UMR 5251, 33400 Talence, France INRIA Bordeaux Sud Ouest, team CQFD, 33400 Talence, France
Laurence Marsalle
Affiliation:
Univ. Lille 1, Laboratoire Paul Painlevé, UMR 8524, 59655 Villeneuve d’Ascq, France CNRS, Laboratoire Paul Painlevé, UMR 8524, 59655 Villeneuve d’Ascq, France. benoite.desaporta@math.u-bordeaux1.fr
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Abstract

This paper presents a new model of asymmetric bifurcating autoregressive process withrandom coefficients. We couple this model with a Galton−Watson tree to take into account possiblymissing observations. We propose least-squares estimators for the various parameters ofthe model and prove their consistency, with a convergence rate, and asymptotic normality.We use both the bifurcating Markov chain and martingale approaches and derive new resultsin both these frameworks.

Keywords

Autoregressive processbranching processmissing dataleast squares estimationlimit theoremsbifurcating Markov chainmartingale

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Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 18 , 2014 , pp. 365 - 399
Copyright
© EDP Sciences, SMAI 2014

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