Electronic Journal of Probability

Asymptotic Analysis for Bifurcating AutoRegressive Processes via a Martingale Approach

Bernard Bercu, Benoîte de Saporta, and Anne Gégout-Petit

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We study the asymptotic behavior of the least squares estimators of the unknown parameters of general pth-order bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process, namely conditional pair-wise independence and suitable moment conditions, we establish the almost sure convergence of our estimators together with the quadratic strong law and the central limit theorem. All our analysis relies on non-standard asymptotic results for martingales.

Article information

Electron. J. Probab., Volume 14 (2009), paper no. 87, 2492-2526.

Accepted: 11 November 2009
First available in Project Euclid: 1 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F15: Strong theorems
Secondary: 60F05: Central limit and other weak theorems 60G42: Martingales with discrete parameter

bifurcating autoregressive process tree-indexed times series martingales least squares estimation almost sure convergence quadratic strong law central limit theorem

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Bercu, Bernard; de Saporta, Benoîte; Gégout-Petit, Anne. Asymptotic Analysis for Bifurcating AutoRegressive Processes via a Martingale Approach. Electron. J. Probab. 14 (2009), paper no. 87, 2492--2526. doi:10.1214/EJP.v14-717. https://projecteuclid.org/euclid.ejp/1464819548

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