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Joint exceedances of the ARCH process

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

M. Ivette Gomes ,
Laurens de Haan  and
Dinis Pestana
M. Ivette Gomes*
Affiliation:
Universidade de Lisboa
Laurens de Haan*
Affiliation:
Erasmus University of Rotterdam
Dinis Pestana*
Affiliation:
Universidade de Lisboa
*
∗ Postal address: CEAUL and DEIO (FUCL), Universidade de Lisboa, Lisboa 1749-016, Portugal
∗∗ Postal address: Econometric Institute, Erasmus University of Rotterdam, PO Box 1738, NL 3000 DR Rotterdam, The Netherlands. Email address: [email protected]
∗ Postal address: CEAUL and DEIO (FUCL), Universidade de Lisboa, Lisboa 1749-016, Portugal
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Abstract

We examine the joint finite structure of extremes of the ARCH process and find an unexpected phenomenon: when assessing probabilities of failure during some finite time interval in the future, the extremal index seems not to be the object to look at. Two possible ramifications of this phenomenon are put forward.

Keywords

ARCH processregular variationstatistics of extremes

MSC classification

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 60G10: Stationary processes 60G17: Sample path properties
Type
Short Communications
Information
Journal of Applied Probability , Volume 41 , Issue 3 , September 2004 , pp. 919 - 926
Copyright
Copyright © Applied Probability Trust 2004 

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