Bernoulli

  • Bernoulli
  • Volume 9, Number 4 (2003), 617-657.

Extreme quantile estimation for dependent data, with applications to finance

Holger Drees

Full-text: Open access

Abstract

The asymptotic normality of a class of estimators for extreme quantiles is established under mild structural conditions on the observed stationary β-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. The theory is then applied to a time series of stock index returns. Finally, the finite-sample behaviour 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.

Article information

Source
Bernoulli, Volume 9, Number 4 (2003), 617-657.

Dates
First available in Project Euclid: 15 October 2003

Permanent link to this document
https://projecteuclid.org/euclid.bj/1066223272

Digital Object Identifier
doi:10.3150/bj/1066223272

Mathematical Reviews number (MathSciNet)
MR1996273

Zentralblatt MATH identifier
1040.62077

Keywords
ARMA model β-mixing confidence interval extreme quantiles GARCH model tail empirical quantile function time series

Citation

Drees, Holger. Extreme quantile estimation for dependent data, with applications to finance. Bernoulli 9 (2003), no. 4, 617--657. doi:10.3150/bj/1066223272. https://projecteuclid.org/euclid.bj/1066223272


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