The notion of $ψ$-weak dependence and its applications to bootstrapping time series

Details The notion of $ψ$-weak dependence and its applications to bootstrapping time series The notion of $ψ$-weak dependence and its applications to bootstrapping time series

2008-06-26

arxiv.org/abs/0806.4263v1

Probability Surveys 2008, Vol. 5, 146-168

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/06-PS086 the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of

Scientific paper

10.1214/06-PS086

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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