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Analyse asymptotique des processus autorégressifs de bifurcation par des méthodes de martingales.

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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https://hal.archives-ouvertes.fr/hal-00325874
Contributor : Anne Gégout-Petit <>
Submitted on : Tuesday, September 30, 2008 - 4:09:59 PM
Last modification on : Wednesday, December 5, 2018 - 9:02:05 AM

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  • HAL Id : hal-00325874, version 1

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Anne Gégout-Petit, Benoîte de Saporta, Bernard Bercu. Analyse asymptotique des processus autorégressifs de bifurcation par des méthodes de martingales.. Journées MAS de la SMAI, Aug 2008, Rennes, France. ⟨hal-00325874⟩

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