Weakly dependent chains with infinite memory

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:118

Article

Doukhan, Paul^1,2  Wintenberger, Olivier¹ 

[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

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

DOI  :  10.1016/j.spa.2007.12.004

来源: Elsevier

【 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.

【 授权许可】

Free