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Name: Sebastian Neblung

Talk Title: Cluster based estimator for the spectral tail process

Abstract: A new type of estimator for the spectral tail process of a regularly varying time series is introduced. The approach is based on the time change formula and a equivalent characterizing invariance property of the spectral tail process introduced by [3]. Using a projection technique, this property is fully exploited to define the new estimator. We state uniform asymptotic normality of this projection based estimator using sliding blocks limit theory of [2]. Results of a simulation study illustrate that the new procedure provides a more stable performance than previously proposed estimators. In particular, the new estimator often has a smaller variance. This talk is based on joint work with Holger Drees and Anja Janßen [1]. References: [1] Drees, H., Janßen, A. and Neblung, S. (2021), ‘Cluster based inference for extremes of time series’, arXiv preprint: 2103.08512 [2] Drees, H. and Neblung, S. (2021), ‘Asymptotics for sliding blocks estimators of rare events’, Bernoulli. to appear. [3] Janßen, A. (2019), ‘Spectral tail processes and max-stable approximations of multivariate regularly varying time series’, Stochastic Processes and Their Applications 129 (6), 1993–2009.

This talk is a contributed talk at EVA 2021.