Extreme Value Theory for Time Series
Models with Power-Law Tails
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Beschreibung
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.
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
Autor*in
Thomas Mikosch
Themen in »Extreme Value Theory for Time Series«
heavy-tail phenomena Modeling extremal events time series cluster phenomena big jump principle
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“This is a comprehensive and clearly written monograph, which both consolidates existing knowledge and extends it in significant directions. The exposition is careful and well motivated, with many examples, making it accessible both to newcomers and to readers already familiar with the basics of extreme-value theory. This monograph situates itself naturally among the well-known references in the field of extreme value theory. The book will become an important reference for researchers and graduate students interested in extremes ... .” (Zakhar Kabluchko, Mathematical Reviews, February, 2026)
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