Cluster based inference for extremes of time series
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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.
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.
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![Prof. Dr. Anja Janßen Prof. Dr. Anja Janßen](/static/gfx/pl/39961~mc.jpg?v=1637701641)
Prof. Dr. Anja Janßen
Otto-von-Guericke-Universität Magdeburg
Institut für Mathematische Stochastik
Universitätsplatz 2
39106
Magdeburg
Tel.:+49 391 6758651
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