Kulik R., Soulier P. Heavy-Tailed Time Series

Springer, 2020. — 677 p. — (Springer Series in Operations Research and Financial Engineering). — ISBN: 978-1-0716-0735-0.This book aims to present a comprehensive, self-contained, and concise overview of extreme value theory for time series, incorporating the latest research trends alongside classical methodology. Appropriate for graduate coursework or professional reference, the book requires a background in extreme value theory for i.i.d. data and basics of time series.Regularly varying random variables
Regularly varying random vectors
Dealing with extremal independence
Regular variation of series and random sums
Regularly varying time series
Convergence of clusters
Point process convergence
Convergence to stable and extremal processes
The tail empirical and quantile processes
Estimation of cluster functionals
Estimation for extremally independent time series
Bootstrap
Max-stable processes
Markov chains
Moving averages
Long memory processes