Mathématiques et Applications

Stochastic Models for Time Series

Authors: Doukhan, Paul

  • Offers mathematically oriented statisticians tools for studying non-linear time-series
  • Discusses moment based techniques  
  • Richly illustrated with examples and simulations
  • Provides material for mathematicians entering the field of non-linear time series
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eBook $59.99
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  • ISBN 978-3-319-76938-7
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Softcover $79.99
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  • ISBN 978-3-319-76937-0
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About this Textbook

This book presents essential tools for modelling non-linear time series. The first part of the book describes the main standard tools of probability and statistics that directly apply to the time series context to obtain a wide range of modelling possibilities. Functional estimation and bootstrap are discussed, and stationarity is reviewed. The second part describes a number of tools from Gaussian chaos and proposes a tour of linear time series models. It goes on to address nonlinearity from polynomial or chaotic models for which explicit expansions are available, then turns to Markov and non-Markov linear models and discusses Bernoulli shifts time series models. Finally, the volume focuses on the limit theory, starting with the ergodic theorem, which is seen as the first step for statistics of time series. It defines the distributional range to obtain generic tools for limit theory under long or short-range dependences (LRD/SRD) and explains examples of LRD behaviours. More general techniques (central limit theorems) are described under SRD; mixing and weak dependence are also reviewed. In closing, it describes moment techniques together with their relations to cumulant sums as well as an application to kernel type estimation.The appendix reviews basic probability theory facts and discusses useful laws stemming from the Gaussian laws as well as the basic principles of probability, and is completed by R-scripts used for the figures. Richly illustrated with examples and simulations, the book is recommended for advanced master courses for mathematicians just entering the field of time series, and statisticians who want more mathematical insights into the background of non-linear time series.

 

About the authors

Paul Doukhan is a Professor at the University of Cergy-Pontoise, Paris. He is an established researcher in the area of non-linear time series. Chiefly focusing on the dependence of stochastic processes, he has published a large number of methodological research papers and authored several books in this research area.

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Table of contents (13 chapters)

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-3-319-76938-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA in USD
  • ISBN 978-3-319-76937-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Stochastic Models for Time Series
Authors
Series Title
Mathématiques et Applications
Series Volume
80
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-76938-7
DOI
10.1007/978-3-319-76938-7
Softcover ISBN
978-3-319-76937-0
Series ISSN
1154-483X
Edition Number
1
Number of Pages
XX, 308
Number of Illustrations and Tables
19 b/w illustrations, 10 illustrations in colour
Topics