Which extreme values are really extreme?
Which extreme values are really extreme?
We define the extreme values of any random sample of size n from a distribution function F as the observations exceeding a threshold and following a type of generalized Pareto distribution (GPD) involving the tail index of F. The threshold is the order statistic that minimizes a Kolmogorov-Smirnov statistic between the empirical distribution of the corresponding largest observations and the corresponding GPD. To formalize the definition we use a semiparametric bootstrap to test the corresponding GPD approximation. Finally, we use our methodology to estimate the tail index and value at risk (VaR) of some financial indexes of major stock markets.
boostrap, extreme values, goodness of fit test, hill estimator, pickands theorem, var
349-369
Gonzalo, J.
25fd9627-b2f7-41a2-b9f0-c9f8ebdfad16
Olmo, J.
706f68c8-f991-4959-8245-6657a591056e
2004
Gonzalo, J.
25fd9627-b2f7-41a2-b9f0-c9f8ebdfad16
Olmo, J.
706f68c8-f991-4959-8245-6657a591056e
Gonzalo, J. and Olmo, J.
(2004)
Which extreme values are really extreme?
Journal of Financial Econometrics, 2 (3), .
(doi:10.1093/jjfinec/nbh014).
Abstract
We define the extreme values of any random sample of size n from a distribution function F as the observations exceeding a threshold and following a type of generalized Pareto distribution (GPD) involving the tail index of F. The threshold is the order statistic that minimizes a Kolmogorov-Smirnov statistic between the empirical distribution of the corresponding largest observations and the corresponding GPD. To formalize the definition we use a semiparametric bootstrap to test the corresponding GPD approximation. Finally, we use our methodology to estimate the tail index and value at risk (VaR) of some financial indexes of major stock markets.
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Published date: 2004
Keywords:
boostrap, extreme values, goodness of fit test, hill estimator, pickands theorem, var
Organisations:
Economics
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Local EPrints ID: 348643
URI: http://eprints.soton.ac.uk/id/eprint/348643
ISSN: 1479-8409
PURE UUID: 891ce932-a9b8-48cd-8ae8-14ef303d029b
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Date deposited: 04 Mar 2013 13:27
Last modified: 15 Mar 2024 03:46
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Author:
J. Gonzalo
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