Extreme Value Theory for Time Series: Models with Power-Law Tails (Hardcover, 2024)

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.