Volume 18, 2014
|Page(s)||365 - 399|
|Published online||03 October 2014|
Random coefficients bifurcating autoregressive processes
1 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
2 Univ. Bordeaux, IMB, UMR 5251, 33400 Talence, France CNRS, IMB, UMR 5251, 33400 Talence, France INRIA Bordeaux Sud Ouest, team CQFD, 33400 Talence, France
3 Univ. Lille 1, Laboratoire Paul Painlevé, UMR 8524, 59655 Villeneuve d’Ascq, France CNRS, Laboratoire Paul Painlevé, UMR 8524, 59655 Villeneuve d’Ascq, France
Revised: 3 May 2013
This paper presents a new model of asymmetric bifurcating autoregressive process with random coefficients. We couple this model with a Galton−Watson tree to take into account possibly missing observations. We propose least-squares estimators for the various parameters of the 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 results in both these frameworks.
Mathematics Subject Classification: 60J05 / 60J80 / 62M05 / 62F12 / 60G42 / 92D25
Key words: Autoregressive process / branching process / missing data / least squares estimation / limit theorems / bifurcating Markov chain / martingale
© EDP Sciences, SMAI 2014
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