Electronic Journal of Statistics

A sliding blocks estimator for the extremal index

Christian Y. Robert, Johan Segers, and Christopher A.T. Ferro

Full-text: Open access

Abstract

In extreme value statistics for stationary sequences, blocks estimators are usually constructed by using disjoint blocks because exceedances over high thresholds of different blocks can be assumed asymptotically independent. In this paper we focus on the estimation of the extremal index which measures the degree of clustering of extremes. We consider disjoint and sliding blocks estimators and compare their asymptotic properties. In particular we show that the sliding blocks estimator is more efficient than the disjoint version and has a smaller asymptotic bias. Moreover we propose a method to reduce its bias when considering sufficiently large block sizes.

Article information

Source
Electron. J. Statist., Volume 3 (2009), 993-1020.

Dates
First available in Project Euclid: 21 September 2009

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1253539754

Digital Object Identifier
doi:10.1214/08-EJS345

Mathematical Reviews number (MathSciNet)
MR2540849

Zentralblatt MATH identifier
1326.60075

Subjects
Primary: 60G70: Extreme value theory; extremal processes 62E20: Asymptotic distribution theory
Secondary: 62G20: Asymptotic properties 62G32: Statistics of extreme values; tail inference

Keywords
Clusters of extremes extremal index FTSE 100 intervals estimator max-autoregressive process moving maximum process maximal correlation coefficient mixing coefficient sample maximum stationary time series

Citation

Robert, Christian Y.; Segers, Johan; Ferro, Christopher A.T. A sliding blocks estimator for the extremal index. Electron. J. Statist. 3 (2009), 993--1020. doi:10.1214/08-EJS345. https://projecteuclid.org/euclid.ejs/1253539754


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