Asymptotic analysis for bifurcating autoregressive processes via a martingale approach
Bernard Bercu, Université de Bordeaux, IMB, CNRS, UMR 5251, and INRIA Bordeaux, team CQFD, Fran
Benoîte de Saporta, Université de Bordeaux, GREThA, CNRS, UMR 5113, IMB, CNRS, UMR 5251, and INRIA B
Anne Gégout-Petit, Université de Bordeaux, IMB, CNRS, UMR 5251, and INRIA Bordeaux, team CQFD, Fran
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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