Resampling procedures for a more reliable extremal index estimation

Dora Prata Gomes, M. Manuela Neves

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

Extreme value theory (EVT) deals essentially with the estimation of parameters of extreme or rare events. One important parameter in EVT, which measures the amount of clustering in the extremes of a stationary sequence, is the extremal index. It needs to be adequately estimated, not only by itself but also due to its influence on other parameters such as a high quantile, return period or expected shortfall. This chapter discusses some classical estimators of extremal index and their asymptotic properties. It illustrates the challenges that appear for finite samples and discusses the generalized jackknife methodology that has shown to give good results in extreme value theory. The chapter provides an extensive simulation study and shows some results of the study. Finally, it applies a heuristic procedure, based on a stability criterion, to some simulated samples to estimate the extremal index.

Original languageEnglish
Title of host publicationData Analysis and Applications 4: Financial Data Analysis and Methods
EditorsAndreas Makrides, Alex Karagrigoriou, Christos H. Skiadas
PublisherWiley
Chapter6
Pages89-101
Number of pages13
ISBN (Electronic)9781119721611
ISBN (Print)9781786306241
DOIs
Publication statusPublished - 18 Apr 2020

Keywords

  • Extremal index
  • Extreme value theory
  • Heuristic procedure
  • Jackknife methodology

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