Weakly dependent chains with infinite memory

被引：79

作者：

Doukhan, Paul ^{[1
,2
]}

Wintenberger, Olivier ^{[1
]}

机构：

[1] Univ Paris 01, CNRS, Ctr Econ Sorbonne, SAMOS MATISSE Stat Appl & MOdelisat Stochast, F-75634 Paris 13, France

[2] Stat Lab, LS CREST, F-92240 Malakoff, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2008年 / 118卷 / 11期

关键词：

Time series; Weak dependence; Central limit theorems; Uniform laws of large numbers; Strong invariance principles;

D O I：

10.1016/j.spa.2007.12.004

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 prove the existence of a weakly dependent strictly stationary solution of the equation X-t = F(Xt-1, Xt-2, Xt-3....;zeta(t)) W called a chain with infinite memory. Here the innovations zeta(t) constitute an independent and identically distributed sequence of random variables. The function F takes values in some Banach space and satisfies a Lipschitz-type condition. We also study the interplay between the existence of moments, the rate of decay of the Lipschitz coefficients of the function F and the weak dependence properties. From these weak dependence properties, we derive strong laws of large number, a central limit theorem and a strong invariance principle. (C) 2007 Elsevier B.V. All rights reserved.

引用

页码：1997 / 2013

页数：17

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[1] NON-STRONG MIXING AUTOREGRESSIVE PROCESSES [J].