Details
Extreme Value Theory for Time Series
Models with Power-Law TailsSpringer Series in Operations Research and Financial Engineering
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235,39 € |
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| Verlag: | Springer |
| Format: | |
| Veröffentl.: | 02.08.2024 |
| ISBN/EAN: | 9783031591563 |
| Sprache: | englisch |
| Anzahl Seiten: | 743 |
Dieses eBook enthält ein Wasserzeichen.
Beschreibungen
<p>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.</p>
<p>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.</p>
<p>The remaining chapters focus on the impact of heavy tails on time series, including the study of extremal cluster phenomena through point process techniques.</p>
<p>A major part of the book investigates how extremal dependence alters the limit structure of sample means, maxima, order statistics, sample autocorrelations. </p>
<p>This text illuminates the theory through hundreds of examples and as many graphs showcasing its applications to real-life financial and simulated data.</p>
<p>The book can serve as a text for PhD and Master courses on applied probability, extreme value theory, and time series analysis.</p>
<p>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.</p>
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<p>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.</p>
<p>The remaining chapters focus on the impact of heavy tails on time series, including the study of extremal cluster phenomena through point process techniques.</p>
<p>A major part of the book investigates how extremal dependence alters the limit structure of sample means, maxima, order statistics, sample autocorrelations. </p>
<p>This text illuminates the theory through hundreds of examples and as many graphs showcasing its applications to real-life financial and simulated data.</p>
<p>The book can serve as a text for PhD and Master courses on applied probability, extreme value theory, and time series analysis.</p>
<p>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.</p>
<p> </p>
<p> </p>
<p>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.</p>
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
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