Asymptotic analysis for bifurcating autoregressive processes via a martingale approach

2008/07/03 by Bernard Bercu, Bercu, Bernard, Benoite de Saporta +4
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60F05 #60F15 #60G42 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Statistical Methods and Inference #Statistics Theory (math.ST) #math.PR #math.ST #msc:60F05 #msc:60F15 #msc:60G42 #stat.TH

paper · pdf · doi:10.48550/arxiv.0807.0528

openalex publication_date 2008/07/03 · arxiv created 2009/06/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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