Weakly dependent chains with infinite memory

Paul Doukhan and Olivier Wintenberger

Stochastic Processes and their Applications, 2008, vol. 118, issue 11, 1997-2013

Abstract: We prove the existence of a weakly dependent strictly stationary solution of the equation Xt=F(Xt-1,Xt-2,Xt-3,...;[xi]t) called a chain with infinite memory. Here the innovations [xi]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.

Keywords: Time; series; Weak; dependence; Central; limit; theorems; Uniform; laws; of; large; numbers; Strong; invariance; principles (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (42)

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