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Extreme Value Theory for Time Series

Models with Power-Law Tails

  • Book
  • Sep 2024


  • Can easily be used for a semester course on extremes for time series at the Master or PhD level
  • Provides a gentle introduction to extreme value theory for heavy-tailed time series
  • Contains a rich toolbox for the heavy-tail and dependence modeler

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About this book

This book deals with extreme value theory for univariate and multivariate time series models characterized by power-law tails. These include the classical ARMA models with heavy-tailed noise and financial econometrics models such as the GARCH and stochastic volatility models.

Rigorous descriptions of power-law tails are provided through the concept of regular variation. Several chapters are devoted to the exploration of regularly varying structures.

The remaining chapters focus on the impact of heavy tails on time series, including the study of extremal cluster phenomena through point process techniques.

A major part of the book investigates how extremal dependence alters the limit structure of sample means, maxima, order statistics, sample autocorrelations. 

This text illuminates the theory through hundreds of examples and as many graphs showcasing its applications to real-life financial and simulated data.

The book can serve as a text for PhD and Master courses on applied probability, extreme value theory, and time series analysis.

It is a unique reference source for the heavy-tail modeler. Its reference quality is enhanced by an exhaustive bibliography, annotated by notes and comments making the book broadly and easily accessible.




  • heavy-tail phenomena
  • Modeling extremal events
  • time series
  • cluster phenomena
  • big jump principle

Authors and Affiliations

  • Dept of Mathematics, University of Copenhagen, Copenhagen, Denmark

    Thomas Mikosch

  • Laboratoire de Probabilités, Statistique et Modélisation, Sorbonne Université, PARIS, France

    Olivier Wintenberger

Bibliographic Information

  • Book Title: Extreme Value Theory for Time Series

  • Book Subtitle: Models with Power-Law Tails

  • Authors: Thomas Mikosch, Olivier Wintenberger

  • Series Title: Springer Series in Operations Research and Financial Engineering

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024

  • Hardcover ISBN: 978-3-031-59155-6Due: 18 September 2024

  • Softcover ISBN: 978-3-031-59158-7Due: 18 September 2025

  • eBook ISBN: 978-3-031-59156-3Due: 18 September 2024

  • Series ISSN: 1431-8598

  • Series E-ISSN: 2197-1773

  • Edition Number: 1

  • Number of Pages: XXVI, 762

  • Number of Illustrations: 2 b/w illustrations, 81 illustrations in colour

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