Asymptotic Analysis for Bifurcating Autoregressive Processes via a martingale approach

Abstract : We study the least-square (LS) estimator of the unknown parameters of a bifurcating auto-regressive process (BAR). Under very weak assumptions on the noise sequence (namely conditional pair-wise independence and moments of order $4$), we derive a precise rate of convergence for the LS estimator, as well as a quadratic strong law and a central limit theorem. Our main tool is martingale theory. However, standard results do not apply directly, as the martingales involved here have a special form and an exponential growth rate.
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Conference papers
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https://hal.archives-ouvertes.fr/hal-00325866
Contributor : Anne Gégout-Petit <>
Submitted on : Tuesday, September 30, 2008 - 4:00:06 PM
Last modification on : Wednesday, December 5, 2018 - 9:02:05 AM

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  • HAL Id : hal-00325866, version 1

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Anne Gégout-Petit, Benoîte de Saporta, Bernard Bercu. Asymptotic Analysis for Bifurcating Autoregressive Processes via a martingale approach. Joint Meeting of the Statistical Society of Canada and the Société Française de Statistique, May 2008, Ottawa, Canada. ⟨hal-00325866⟩

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