Heavy-Tailed Time Series

1. Auflage 2020
ISBN: 978-1-0716-0735-0
Verlag: Springer

Buch, Englisch, 681 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1337 g

Reihe: 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 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.

Zielgruppe

Graduate

Autoren/Hrsg.

Soulier, Philippe

Kulik, Rafal

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse

Inhaltsverzeichnis

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.

Über Autor(innen)

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.