Journal
ELECTRONIC JOURNAL OF STATISTICS
Volume 3, Issue -, Pages 993-1020Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/08-EJS345
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
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Funding
- IAP research network of the Belgian government [P6/03]
- Academic universitaire Louvain [07/12/002]
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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.
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