ENGLISH

Weak dependence: With examples and applications

By Jérôme Dedecker , Paul Doukhan , Gabriel Lang , José Rafael Leon , Sana Louhichi , Clémentine Prieur

Book information

Publisher
Springer
Year
2007
ISBN
0387699511, 978-0-387-69951-6
LCC
QA273.18 .W43 2007
Open Library ID
OL18500537M
Language
english
Format
PDF
Filesize
2 MB (2333180 bytes)
Series
Lecture Notes in Statistics 0190
Pages
323\323
Library
Kolxo3
Time added
2009-07-20 03:45:11

Description

This monograph is aimed at developing Doukhan/Louhichi's (1999) idea to measure asymptotic independence of a random process. The authors propose various examples of models fitting such conditions such as stable Markov chains, dynamical systems or more complicated models, nonlinear, non-Markovian, and heteroskedastic models with infinite memory. Most of the commonly used stationary models fit their conditions. The simplicity of the conditions is also their strength. The main existing tools for an asymptotic theory are developed under weak dependence. They apply the theory to nonparametric statistics, spectral analysis, econometrics, and resampling. The level of generality makes those techniques quite robust with respect to the model. The limit theorems are sometimes sharp and always simple to apply. The theory (with proofs) is developed and the authors propose to fix the notation for future applications. A large number of research papers deals with the present ideas; the authors as well as numerous other investigators participated actively in the development of this theory. Several applications are still needed to develop a method of analysis for (nonlinear) times series and they provide here a strong basis for such studies.

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