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020 _a9783031591563
_9978-3-031-59156-3
024 7 _a10.1007/978-3-031-59156-3
_2doi
050 4 _aQA273.A1-274.9
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100 1 _aMikosch, Thomas.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_981790
245 1 0 _aExtreme Value Theory for Time Series
_h[electronic resource] :
_bModels with Power-Law Tails /
_cby Thomas Mikosch, Olivier Wintenberger.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXVI, 766 p. 83 illus., 81 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Series in Operations Research and Financial Engineering,
_x2197-1773
505 0 _aIntroduction -- 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.
520 _aThis 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. .
650 0 _aProbabilities.
_965724
650 0 _aMathematical statistics.
_967233
650 1 4 _aApplied Probability.
_965727
650 2 4 _aMathematical Statistics.
_967233
700 1 _aWintenberger, Olivier.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_981791
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031591556
776 0 8 _iPrinted edition:
_z9783031591570
776 0 8 _iPrinted edition:
_z9783031591587
830 0 _aSpringer Series in Operations Research and Financial Engineering,
_x2197-1773
_976963
856 4 0 _uhttps://doi.org/10.1007/978-3-031-59156-3
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
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