Asymptotic analysis for bifurcating autoregressive processes via a martingale approach

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00293341
Contributor : Benoîte de Saporta <>
Submitted on : Friday, July 4, 2008 - 11:10:49 AM
Last modification on : Wednesday, December 5, 2018 - 9:02:07 AM

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  • HAL Id : hal-00293341, version 1
  • ARXIV : 0807.0528

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Bernard Bercu, Benoîte de Saporta, Anne Gegout-Petit. Asymptotic analysis for bifurcating autoregressive processes via a martingale approach. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2009, 14 (87), pp.2492-2526. ⟨hal-00293341⟩

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