Heavy-tailed Time Series (springer Series In Operations Research And Financial Engineering)

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 Unique 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 Weak And Vague Convergence. Front Matter ....Pages i-xix Front Matter ....Pages 1-1 Regularly varying random variables (Rafał Kulik, Philippe Soulier)....Pages 3-21 Regularly varying random vectors (Rafał Kulik, Philippe Soulier)....Pages 23-52 Dealing with extremal independence (Rafał Kulik, Philippe Soulier)....Pages 53-73 Regular variation of series and random sums (Rafał Kulik, Philippe Soulier)....Pages 75-99 Regularly varying time series (Rafał Kulik, Philippe Soulier)....Pages 101-145 Front Matter ....Pages 147-147 Convergence of clusters (Rafał Kulik, Philippe Soulier)....Pages 149-171 Point process convergence (Rafał Kulik, Philippe Soulier)....Pages 173-205 Convergence to stable and extremal processes (Rafał Kulik, Philippe Soulier)....Pages 207-233 The tail empirical and quantile processes (Rafał Kulik, Philippe Soulier)....Pages 235-263 Estimation of cluster functionals (Rafał Kulik, Philippe Soulier)....Pages 265-312 Estimation for extremally independent time series (Rafał Kulik, Philippe Soulier)....Pages 313-332 Bootstrap (Rafał Kulik, Philippe Soulier)....Pages 333-345 Front Matter ....Pages 347-347 Max-stable processes (Rafał Kulik, Philippe Soulier)....Pages 349-371 Markov chains (Rafał Kulik, Philippe Soulier)....Pages 373-423 Moving averages (Rafał Kulik, Philippe Soulier)....Pages 425-452 Long memory processes (Rafał Kulik, Philippe Soulier)....Pages 453-487 Back Matter ....Pages 489-681 "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 chapters 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"--Back cover