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Preprint (Vorabdruck) zugänglich unter
URN: urn:nbn:de:bsz:291-scidok-43932
URL: http://scidok.sulb.uni-saarland.de/volltexte/2011/4393/


Extreme quantile estimation for dependent data with applications to finance

Drees, Holger

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Freie Schlagwörter (Englisch): confidence interval , GARCH model , tail empirical quantile function
Institut: Fachrichtung 6.1 - Mathematik
DDC-Sachgruppe: Mathematik
Dokumentart: Preprint (Vorabdruck)
Schriftenreihe: Preprint / Fachrichtung Mathematik, Universit├Ąt des Saarlandes
Bandnummer: 68
Sprache: Englisch
Erstellungsjahr: 2002
Publikationsdatum: 02.12.2011
Kurzfassung auf Englisch: The asymptotic normality of a class of estimators for extreme quantiles is established under mild structural conditions on the observed stationary \beta-mixing time series. Consistent estimators of the asymptotic variance are introduced, which render possible the construction of asymptotic confidence intervals for the extreme quantiles. Moreover, it is shown that many well-known time series models satisfy our conditions. Then the theory is applied to a time series of returns of a stock index. Finally, the finite sample behavior of the proposed confidence intervals is examined in a simulation study. It turns out that for most time series models under consideration the actual coverage probability is pretty close to the nominal level if the sample fraction used for estimation is chosen appropriately.
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