Weak convergence of a pseudo maximum likelihood estimator for the extremal index

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dc.contributor.authorBerghaus, Betina
dc.contributor.authorBücher, Axel
dc.date.accessioned2016-09-19T10:06:11Z
dc.date.available2016-09-19T10:06:11Z
dc.date.issued2016
dc.description.abstractThe 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.en
dc.identifier.urihttp://hdl.handle.net/2003/35214
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-17258
dc.language.isoende
dc.relation.ispartofseriesDiscussion Paper / SFB823;47, 2016en
dc.subjectclusters of extremesen
dc.subjectblock maximaen
dc.subjectmixing coefficientsen
dc.subjectstationary time seriesen
dc.subjectextremal indexen
dc.subject.ddc310
dc.subject.ddc330
dc.subject.ddc620
dc.titleWeak convergence of a pseudo maximum likelihood estimator for the extremal indexen
dc.typeTextde
dc.type.publicationtypeworkingPaperde
dcterms.accessRightsopen access

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Sonderforschungsbereich (SFB) 823