Authors: Berghaus, Betina
Bücher, Axel
Title: Weak convergence of a pseudo maximum likelihood estimator for the extremal index
Language (ISO): en
Abstract: The extremes of a stationary time series typically occur in clusters. A primary measure for this phenomenon is the extremal index, representing the reciprocal of the expected cluster size. Both a disjoint and a sliding blocks estimator for the extremal index are analyzed in detail. In contrast to many competitors, the estimators only depend on the choice of one parameter sequence. We derive an asymptotic expansion, prove asymptotic normality and show consistency of an estimator for the asymptotic variance. Explicit calculations in certain models and a finite-sample Monte Carlo simulation study reveal that the sliding blocks estimator is outperforming other blocks estimators, and that it is competitive to runs- and inter-exceedance estimators in various models. The methods are applied to a variety of financial time series.
Subject Headings: clusters of extremes
block maxima
mixing coefficients
stationary time series
extremal index
URI: http://hdl.handle.net/2003/35214
http://dx.doi.org/10.17877/DE290R-17258
Issue Date: 2016
Appears in Collections:Sonderforschungsbereich (SFB) 823

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