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Abstract:
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The estimation of the tail index of distributions with heavy, Pareto-type tails is an old problem which continues to pose challenges. We propose a novel approach for estimating the tail index, based on the max self-similarity scaling of block maxima. The method exploits the increasing lack of dependence of maxima over large size blocks, which proves useful for dependent, time series data. We establish the consistency of the proposed max-spectrum estimator for certain classes of dependent time series and demonstrate its robustness to short-lived contaminations in the data. The max-spectrum estimator exhibits linear computational time and memory complexity and can be calculated in a sequential manner, that makes it particularly well suited both for massive, as well as streaming data sets. It also provides a natural time-scale perspective in the analysis of heavy-tailed time series.
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