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TitleEstimating the extremal index through local dependence
Author(s)Ferreira, Helena
Ferreira, Marta Susana
KeywordsExtreme value theory
Stationary sequences
Dependence conditions
Extremal index
Issue date2018
PublisherInstitute Henri Poincaré
JournalAnnales de l'Institut Henri Poincaré. B, Probabilités et Statistiques
Abstract(s)The extremal index is an important parameter in the characterization of extreme values of a stationary sequence. Our new estimation approach for this parameter is based on the extremal behavior under the local dependence condition D(k)(un). We compare a process satisfying one of this hierarchy of increasingly weaker local mixing conditions with a process of cycles satisfying the D(2)(un) condition. We also analyze local dependence within moving maxima processes and derive a necessary and sufficient condition for D(k)(un). In order to evaluate the performance of the proposed estimators, we apply an empirical diagnostic for local dependence conditions, we conduct a simulation study and compare with existing methods. An application to a financial time series is also presented.
AccessRestricted access (UMinho)
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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