Cluster based inference for extremes of time series

This is work is part of the Ph.D.-project of Sebastian Neblung, for whom I am the second supervisor.

In this project we introduce a new type of estimator for the spectral tail process of a regularly varying time series. The approach is based on a characterizing invariance property of the spectral tail process which has been derived in Janßen (2019) and is incorporated into the new estimator via a projection technique. Based on the limit results for empirical tail processes developed in Drees & Neblung (2019), we show uniform asymptotic normality of this estimator both in the case of known and unknown index of regular variation. A simulation study illustrates that the new procedure provides an often more stable alternative to previous estimators.