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Inference for clusters of extreme values. (English) Zbl 1065.62091

Summary: Inference for clusters of extreme values of a time series typically requires the identification of independent clusters of exceedances over a high threshold. The choice of the declustering scheme often has a significant effect on estimates of cluster characteristics. We propose an automatic declustering scheme that is justified by an asymptotic result for the times between threshold exceedances. The scheme relies on the extremal index, which we show may be estimated before declustering, and supports a bootstrap procedure for assessing the variability of estimates.

MSC:

62G32 Statistics of extreme values; tail inference
62M09 Non-Markovian processes: estimation
62E20 Asymptotic distribution theory in statistics
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