Heavy-Tailed Time Series

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. Following a brief review of foundational concepts, it progresses linearly through topics in limit theorems and time series models while including historical insights at each chapter’s conclusion. Additionally, the book incorporates complete proofs and exercises with solutions as well as substantive reference lists and appendices, featuring a novel commentary on the theory of vague convergence.

Regular variation.- Regularly varying random variables.- Regularly varying random vectors.- Dealing with extremal independence.- Regular variation of series and random sums.- Regularly varying time series.- Limit theorems.- Convergence of clusters-. Point process convergence.- Convergence to stable and extremal processes.- The tall empirical and quantile processes.- Estimation of cluster functionals.- Estimation for extremally independent time series.- Bootstrap.- Time series models.- Max-stable processes.- Markov chains.- Moving averages.- Long memory processes.- Appendices.