Publication detail

Statistical inference on the local dependence condition of extreme values in a stationary sequence

HOLEŠOVSKÝ, J. FUSEK, M.

Original Title

Statistical inference on the local dependence condition of extreme values in a stationary sequence

Type

journal article in Web of Science

Language

English

Original Abstract

The extremal index is an important characteristic measuring dependence of extreme values in a stationary series. Several new estimators that are mostly based on interexceedance times within the Peaks-over-Threshold model have been recently published. Nevertheless, in many cases these estimators rely on suitable choice of auxiliary parameters and/or are derived under assumptions that are related to validity of the local dependence condition $D^{(k)}(u_n)$. Although the determination of the correct order $k$ in the $D^{(k)}(u_n)$ condition can have major effect on the extremal index estimates, there are not many reliable methods available for this task. In this paper, we present various approaches to assessing validity of the $D^{(k)}(u_n)$ condition including a graphical diagnostics and propose several statistical tests. A simulation study is carried out to determine performance of the statistical tests, particularly the type I and type II errors.

Keywords

Local dependence; extremal index; extreme value theory; clusters

Authors

HOLEŠOVSKÝ, J.; FUSEK, M.

Released

28. 7. 2025

Publisher

Springer

ISBN

1386-1999

Periodical

EXTREMES

Year of study

28

Number

3

State

United States of America

Pages from

557

Pages to

578

Pages count

22

URL

https://link.springer.com/article/10.1007/s10687-025-00513-8

Full text in the Digital Library

http://hdl.handle.net/11012/255408

BibTex

@article{BUT197986,
  author="Jan {Holešovský} and Michal {Fusek}",
  title="Statistical inference on the local dependence condition of extreme values in a stationary sequence",
  journal="EXTREMES",
  year="2025",
  volume="28",
  number="3",
  pages="557--578",
  doi="10.1007/s10687-025-00513-8",
  issn="1386-1999",
  url="https://link.springer.com/article/10.1007/s10687-025-00513-8"
}