The notion of ψ-weak dependence and its applications to bootstrapping time series
Paul Doukhan and Michael H. Neumann
Source: Probab. Surveys Volume 5 (2008), 146-168.
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.
Primary Subjects: 60E15
Secondary Subjects: 62E99
Keywords: Autoregressive processes; autoregressive bootstrap; mixing; weak dependence
Full-text: Open access
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Permanent link to this document: http://projecteuclid.org/euclid.ps/1214491946
Digital Object Identifier: doi:10.1214/06-PS086
Mathematical Reviews number (MathSciNet):
MR2426177
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