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We give an introduction to a notion of weak dependence which is more generalthan mixing and allows to treat for example processes driven by discreteinnovations as they appear with time series bootstrap. As a typical example, weanalyze autoregressive processes and their bootstrap analogues in detail andshow how weak dependence can be easily derived from a contraction property ofthe process. Furthermore, we provide an overview of classes of processespossessing the property of weak dependence and describe important probabilisticresults under such an assumption.

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