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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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819548

Digital Object Identifier
doi:10.1214/EJP.v14-717

Mathematical Reviews number (MathSciNet)
MR2563249

Zentralblatt MATH identifier
1190.60019

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

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

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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