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

Paul Doukhan (1, 2) , Michael Neumann (3)

1 CES - Centre d'économie de la Sorbonne
2 SAMOS - Statistique Appliquée et MOdélisation Stochastique
3 IENA - Institut fur Stochastik Ernst Friedrich-Schiller-Universitat Jena

We give an introduction to the 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.

Mots clés: Autoregressive processes; autoregressive bootstrap; mixing; weak dependence.; weak dependence

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Paul Doukhan, Michael Neumann. The notion of ψ-weak dependence and its applications to bootstrapping time series. Probability Surveys, 2008, 5, pp.146-168. ⟨10.1214/06-PS086⟩. ⟨hal-00141589⟩