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2008 The notion of ψ-weak dependence and its applications to bootstrapping time series
Paul Doukhan, Michael H. Neumann
Probab. Surveys 5: 146-168 (2008). DOI: 10.1214/06-PS086

Abstract

We give an introduction to a notion of weak dependence which is more general than mixing and allows to treat for example processes driven by discrete innovations as they appear with time series bootstrap. As a typical example, we analyze autoregressive processes and their bootstrap analogues in detail and show how weak dependence can be easily derived from a contraction property of the process. Furthermore, we provide an overview of classes of processes possessing the property of weak dependence and describe important probabilistic results under such an assumption.

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Paul Doukhan. Michael H. Neumann. "The notion of ψ-weak dependence and its applications to bootstrapping time series." Probab. Surveys 5 146 - 168, 2008. https://doi.org/10.1214/06-PS086

Information

Published: 2008
First available in Project Euclid: 26 June 2008

zbMATH: 1189.60043
MathSciNet: MR2426177
Digital Object Identifier: 10.1214/06-PS086

Subjects:
Primary: 60E15
Secondary: 62E99

Keywords: autoregressive bootstrap , autoregressive processes , Mixing , Weak dependence

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

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