Automatic declustering of rare events

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The analysis of events with low probability but disastrous impact entails understanding how they cluster in time. We present an automatic three-step procedure for identifying clusters, estimating the cluster size distribution and constructing confidence intervals for the extremal index, which measures the degree of clustering of rare events. The third step combines empirical likelihood and parametric likelihood approaches. Simulations show that our new procedure performs very well for finite samples and outperforms previous methods in constructing confidence intervals for the extremal index when there is clustering in the data, as well as in estimating probabilities for small clusters.

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