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.

• Extreme value theory
• Time series
• extremal processes
• Point processes
• Stable processes
• Statistics of extreme values
• tail inference

• Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada

  Rafal Kulik

• Université Paris X, Nanterre, France

  Philippe Soulier

Rafal Kulik graduated from the University of Wroclaw, Poland. He is currently a Professor at the Department of Mathematics and Statistics, University of Ottawa. His research interests are centered around limit theorems for stochastic  processes with temporal dependence. 

Philippe Soulier graduated from Ecole Normale Supérieure de Paris and obtained his PhD at University Paris XI Orsay. He is Professor of Mathematics at University Paris Nanterre. His main themes of research are long memory processes and extreme value theory.

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