Work

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

Year: 2025

Type: article

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 $$D^{(k)}(u_n)$$ D ( k ) ( u n ) . Although the determination of the correct order k in the $$D^{(k)}(u_n)$$ 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 $$D^{(k)}(u_n)$$ 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.

Source: Extremes

DOI: 10.1007/s10687-025-00513-8

Authors: Jan Holešovský, Michal Fusek

Institution: Brno University of Technology

Language: English

Topic: Probability and Risk Models

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $2,290

Funder: Vysoké Učení Technické v Brně