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El. knyga: Extreme Value Theory for Time Series: Models with Power-Law Tails

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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.





 





 
Introduction.- Part 1 Regular variation of distributions and processes.-
2 The iid univariate benchmark.- 3 Regularly varying random variables and
vectors.- 4 Regularly varying time series.- 5 Examples of regularly varying
stationary processes.- Part 2 Point process convergence and cluster phenomena
of time series.- 6 Clusters of extremes.- 7 Point process convergence for
regularly varying sequences.- 8 Applications of point process convergence.-
Part 3 Infinite variance central limit theory.- 9 Infinite-variance central
limit theory.- 10 Self-normalization, sample autocorrelations and the
extremogram.- Appendix A Point processes.- Appendix B Univariate regular
variation.- Appendix C Vague convergence.- Appendix D Tools.- Appendix E
Multivariate regular variation supplementary results.- Appendix F
Heavy-tail large deviations for sequences of independent random variables and
vectors, and their applications.-references.- index.- List of abbreviations
and symbols.
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