Weak Dependence: With Examples and Applications: With Examples and Applications

Paperback | July 18, 2007

byJérome Dedecker, Paul Doukhan, Gabriel Lang

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This book develops Doukhan/Louhichi's 1999 idea to measure asymptotic independence of a random process. The authors, who helped develop this theory, propose examples of models fitting such conditions: stable Markov chains, dynamical systems or more complicated models, nonlinear, non-Markovian, and heteroskedastic models with infinite memory. Applications are still needed to develop a method of analysis for nonlinear times series, and this book provides a strong basis for additional studies.

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From the Publisher

This book develops Doukhan/Louhichi's 1999 idea to measure asymptotic independence of a random process. The authors, who helped develop this theory, propose examples of models fitting such conditions: stable Markov chains, dynamical systems or more complicated models, nonlinear, non-Markovian, and heteroskedastic models with infinite m...

From the Jacket

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 infinit...

Format:PaperbackDimensions:336 pages, 9.25 × 6.1 × 0 inPublished:July 18, 2007Publisher:Springer New YorkLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0387699511

ISBN - 13:9780387699516

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Table of Contents

Introduction.- Weak dependence.- Models.- Tools for non causal cases.- Tools for causal cases.- Applications of SLLN.- Central limit theorem.- Donsker principles.- Law of the iterated logarithm (LIL).- The empirical process.- Functional estimation.- Spectral estimation.- Econometrics and resampling.

Editorial Reviews

From the reviews:"I appreciate this book as a very welcome and thorough discussion of the actual state-of-the art in the modeling of dependence structures. It provides a large number of motivating examples and applications, rigorous proofs, and valuable intuitions for the willing and mathematically well-trained reader with essential prior knowledge of the mathematical prerequisites of weak dependence . . It is . the book to those researchers already aware of the necessity of the methods discussed here." (Harry Haupt, Advances in Statistical Analysis, Vol. 93, 2009)"This book . provides a detailed description of the notion of weak dependence as well as properties and applications. . Overall the book is neatly written . . the book is very rich in its material as it contains earlier works on dependence and . show a lot of applications of the theory. It also contains a large number of examples and expositions of the idea of weak dependence in models . which provide good insight." (Dimitris Karlis, Zentralblatt MATH, Vol. 1165, 2009)