Electronic Journal of Statistics

A sliding blocks estimator for the extremal index

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

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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

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

First available in Project Euclid: 21 September 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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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