04185nam a22005055i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001900172072001600191072001700207072002300224072001500247072001600262100008500278245013900363250001800502264006900520300006500589336002600654337002600680338003600706347002400742490008100766505100400847520125901851650002603110650003603136650003203172650003603204700009103240710003403331773002603365776003603391776003603427776003603463830008803499856004603587912001403633912001503647999001703662978-3-031-59156-3DE-He21320251030112707.0cr nn 008mamaa240802s2024    sz |    s    |||| 0|eng d  a97830315915639978-3-031-59156-37 a10.1007/978-3-031-59156-32doi 4aQA273.A1-274.9 7aPBT2bicssc 7aPBWL2bicssc 7aMAT0290002bisacsh 7aPBT2thema 7aPBWL2thema1 aMikosch, Thomas.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut98179010aExtreme Value Theory for Time Seriesh[electronic resource] :bModels with Power-Law Tails /cby Thomas Mikosch, Olivier Wintenberger.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXVI, 766 p. 83 illus., 81 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSpringer Series in Operations Research and Financial Engineering,x2197-17730 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.  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. . 0aProbabilities.965724 0aMathematical statistics.96723314aApplied Probability.96572724aMathematical Statistics.9672331 aWintenberger, Olivier.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9817912 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303159155608iPrinted edition:z978303159157008iPrinted edition:z9783031591587 0aSpringer Series in Operations Research and Financial Engineering,x2197-177397696340uhttps://doi.org/10.1007/978-3-031-59156-3  aZDB-2-SMA  aZDB-2-SXMS  c62177d62177