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Extreme residual dependence for random vectors and processes

Part of: Nonparametric inference

Published online by Cambridge University Press:  01 July 2016

Laurens De Haan  and
Chen Zhou
Laurens De Haan*
Affiliation:
Tilburg University and University of Lisbon
Chen Zhou*
Affiliation:
De Nederlandsche Bank and Erasmus University Rotterdam
*
∗ Postal address: Department of Econometrics and Operations Research, Tilburg University, PO Box 90153, 5000LE Tilburg, The Netherlands. Email address: [email protected]
∗∗ Postal address: Economics and Research Division, De Nederlandsche Bank, PO Box 98, 1000AB Amsterdam, The Netherlands. Email address: [email protected]
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Abstract

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A two-dimensional random vector in the domain of attraction of an extreme value distribution G is said to be asymptotically independent (i.e. in the tail) if G is the product of its marginal distribution functions. Ledford and Tawn (1996) discussed a form of residual dependence in this case. In this paper we give a characterization of this phenomenon (see also Ramos and Ledford (2009)), and offer extensions to higher-dimensional spaces and stochastic processes. Systemic risk in the banking system is treated in a similar framework.

Keywords

Asymptotic independenceextreme residual dependencespectral measure

MSC classification

Primary: 62G20: Asymptotic properties
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 43 , Issue 1 , March 2011 , pp. 217 - 242
Copyright
Copyright © Applied Probability Trust 2011 

Footnotes

Supported in part by FCT project PTDC/MAT/112770/2009.

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