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Title: Robust estimation of the extremal index in the context of climate time series Authors:  Katharina Hees - TU Dortmund University (Germany) [presenting]
Abstract: Extreme events of climate time series often occur in clusters, for example, in storms, floods, earthquakes, etc. The most common approach to analyze such serially correlated data is to first identify the clusters and then to proceed with the peaks of the clusters with classical extreme value theory methods. The extremal index $\theta$ plays an important role in the declustering process. One interpretation of this quantity is, for example, that it is the reciprocal of the limiting mean number of exceedances in blocks with at least one exceedance. Another interpretation is that it is the proportion of inter-exceedance times that represent the times between different clusters. Hence, the knowledge of the extremal index allows us to decluster the data by sorting the inter-exceedance times by size and assuming the $\theta$ largest to be the intercluster times (between clusters) and the $(1-\theta)$ smallest to be the intracluster times (within clusters). In the context of climate time series, one is often confronted with outliers. Several methods for the estimation of the extremal index were proposed in the literature, but most of them are not robust with respect to such outliers. We will present a method that is robust, and compare it to existing and well-established extremal index estimators.