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Weak Dependence: With Examples and Applications
Paperback
Series: Lecture Notes in Statistics, Book 190
ISBN13: 9780387699516
Publisher: Springer
Published: Jul 18 2007
Pages: 322
Weight: 1.05
Height: 0.63 Width: 6.61 Depth: 9.15
Language: English
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 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. 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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