Asymptotic analysis for bifurcating autoregressive processes via a martingale approach

被引：24

作者：

Bercu, Bernard ^{[1
,2
]}

de Saporta, Benoite ^{[1
,2
]}

Gegout-Petit, Anne ^{[2
]}

机构：

[1] Univ Bordeaux, IMB, CNRS, GREThA,UMR 5113,UMR 5251, Bordeaux, France

[2] INRIA Bordeaux, Team CQFD, Bordeaux, France

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2009年 / 14卷

关键词：

bifurcating autoregressive process; tree-indexed times series; martingales; least squares estimation; almost sure convergence; quadratic strong law; central limit theorem; MODELS;

D O I：

10.1214/EJP.v14-717

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：2492 / 2526

页数：35

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