HAL : hal-00141589, version 1

DOI : 10.1214/06-PS086

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Probability Surveys 5 (2008) 146-168

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

Paul Doukhan 1, 2, Michael Neumann 3

(2008)

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.

1 :	Centre d'économie de la Sorbonne (CES)
	CNRS : UMR8174 – Université Paris I - Panthéon-Sorbonne
2 :	Statistique Appliquée et MOdélisation Stochastique (SAMOS)
	Université Paris I - Panthéon-Sorbonne
3 :	Institut fur Stochastik Ernst Friedrich-Schiller-Universitat Jena (IENA)
	Universität Jena

Domaine

:

Mathématiques/Statistiques Statistiques/Théorie

Mots Clés : Autoregressive processes – autoregressive bootstrap – mixing – weak dependence.

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Contributeur : Paul Doukhan <>

Soumis le : Jeudi 3 Mai 2007, 11:22:44

Dernière modification le : Jeudi 17 Juillet 2008, 14:25:58