Asymptotic analysis for bifurcating autoregressive processes via a martingale approach

Bernard Bercu, Benoite de Saporta, Anne Gegout-Petit

Published 2008-07-03, updated 2009-06-29Version 2

We study the asymptotic behavior of the least squares estimators of the unknown parameters of 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.