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2009 Asymptotic Analysis for Bifurcating AutoRegressive Processes via a Martingale Approach
Bernard Bercu, Benoîte de Saporta, Anne Gégout-Petit
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Electron. J. Probab. 14: 2492-2526 (2009). DOI: 10.1214/EJP.v14-717


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.


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Bernard Bercu. Benoîte de Saporta. Anne Gégout-Petit. "Asymptotic Analysis for Bifurcating AutoRegressive Processes via a Martingale Approach." Electron. J. Probab. 14 2492 - 2526, 2009.


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

zbMATH: 1190.60019
MathSciNet: MR2563249
Digital Object Identifier: 10.1214/EJP.v14-717

Primary: 60F15
Secondary: 60F05 , 60G42

Keywords: Almost sure convergence , Bifurcating autoregressive process , central limit theorem , Least squares estimation , Martingales , quadratic strong law , tree-indexed times series

Vol.14 • 2009
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