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The notion of \(\psi \)-weak dependence and its applications to bootstrapping time series. (English) Zbl 1189.60043

Summary: 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.

MSC:

60E15 Inequalities; stochastic orderings
62E99 Statistical distribution theory
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