Doukhan, Paul; Neumann, Michael H. The notion of \(\psi \)-weak dependence and its applications to bootstrapping time series. (English) Zbl 1189.60043 Probab. Surv. 5, 146-168 (2008). 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. Cited in 18 Documents MSC: 60E15 Inequalities; stochastic orderings 62E99 Statistical distribution theory Keywords:autoregressive processes; autoregressive bootstrap; mixing; weak dependence PDFBibTeX XMLCite \textit{P. Doukhan} and \textit{M. H. Neumann}, Probab. Surv. 5, 146--168 (2008; Zbl 1189.60043) Full Text: DOI arXiv EuDML