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2009 A sliding blocks estimator for the extremal index
Christian Y. Robert, Johan Segers, Christopher A.T. Ferro
Electron. J. Statist. 3: 993-1020 (2009). DOI: 10.1214/08-EJS345

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.

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

Information

Published: 2009
First available in Project Euclid: 21 September 2009

zbMATH: 1326.60075
MathSciNet: MR2540849
Digital Object Identifier: 10.1214/08-EJS345

Subjects:
Primary: 60G70 , 62E20
Secondary: 62G20 , 62G32

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

Rights: Copyright © 2009 The Institute of Mathematical Statistics and the Bernoulli Society

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