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.

Provides a comprehensive and self-contained overview of extreme value theory for time series Presents concise theoretical analysis of regular variation and weak convergence, with relation to time series Includes complete proofs and exercises with solutions Includes list of open problems to encourage future research?

Autorentext

Jan Beran is a Professor of Statistics at the University of Konstanz (Department of Mathematics and Statistics). After completing his PhD in Mathematics at the ETH Zurich, he worked at several U.S. universities and the University of Zurich. He has a broad range of interests, from long-memory processes and asymptotic theory to applications in finance, biology and musicology. Yuanhua Feng is a Professor of Econometrics at the University of Paderborn's Department of Economics. He previously worked at the Heriot-Watt University, UK, after completing his PhD and postdoctoral studies at the University of Konstanz. His research interests include financial econometrics, time series and semiparametric modeling. Sucharita Ghosh (M.Stat. Indian Statistical Institute; PhD Univ. Toronto) is a statistician at the Swiss Federal Research Institute WSL. She has taught at the University of Toronto, UNC Chapel Hill, Cornell University, the University of Konstanz, University of York and the ETH Zurich. Her research interests include space-time processes, nonparametric curve estimation and empirical transforms. Rafal Kulik is an Associate Professor at the University of Ottawa's Department of Mathematics and Statistics. He has previously taught at the University of Wroclaw, University of Ulm and University of Sydney. His research interests include limit theorems for weakly and strongly dependent random variables, time series analysis and heavy-tailed phenomena, with applications in finance.

Inhalt
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.