04398nam a22005535i 4500 978-3-031-59156-3 DE-He213 20251030112707.0 cr nn 008mamaa 240802s2024 sz | s |||| 0|eng d 9783031591563 978-3-031-59156-3 10.1007/978-3-031-59156-3 doi QA273.A1-274.9 PBT bicssc PBWL bicssc MAT029000 bisacsh PBT thema PBWL thema Mikosch, Thomas. author. aut http://id.loc.gov/vocabulary/relators/aut 81790 Extreme Value Theory for Time Series [electronic resource] : Models with Power-Law Tails / by Thomas Mikosch, Olivier Wintenberger. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XVI, 766 p. 83 illus., 81 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Springer Series in Operations Research and Financial Engineering, 2197-1773 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. 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. . Probabilities. 65724 Mathematical statistics. 67233 Applied Probability. 65727 Mathematical Statistics. 67233 Wintenberger, Olivier. author. aut http://id.loc.gov/vocabulary/relators/aut 81791 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031591556 Printed edition: 9783031591570 Printed edition: 9783031591587 Springer Series in Operations Research and Financial Engineering, 2197-1773 76963 https://doi.org/10.1007/978-3-031-59156-3 ZDB-2-SMA ZDB-2-SXMS 62177 62177