Asymptotic Analysis for Bifurcating AutoRegressive Processes via a Martingale Approach

Bernard Bercu (Université de Bordeaux)
Benoîte de Saporta (Université de Bordeaux)
Anne Gégout-Petit (Université de Bordeaux)

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.

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Pages: 2492-2526

Publication Date: November 11, 2009

DOI: 10.1214/EJP.v14-717

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