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Multiperiod conditional distribution functions for conditionally normal GARCH(1, 1) models

Part of: Distribution theory Applications Stochastic processes Mathematical economics

Published online by Cambridge University Press:  14 July 2016

Raymond Brummelhuis  and
Dominique Guégan
Raymond Brummelhuis*
Affiliation:
Birkbeck College
Dominique Guégan*
Affiliation:
École Normale Supérieure de Cachan
*
∗ Postal address: School of Economics, Mathematics and Statistics, Birkbeck College, University of London, Malet Street, London WC1E 7HX, UK. Email address: r.brummelhuis@statistics.bbk.ac.uk
∗∗ Postal address: Département d'Économie et de Gestion, ENS Cachan, 61 av. du President Wilson, 94235 Cachan Cedex, France. Email address: guegan@ecogest.ens-cachan.fr
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Abstract

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We study the asymptotic tail behavior of the conditional probability distributions of r t+k and r t+1+⋯+r t+k when (r t )t∈ℕ is a GARCH(1, 1) process. As an application, we examine the relation between the extreme lower quantiles of these random variables.

Keywords

Generalized autoregressive heteroskedastic processconditional probability density functionlarge deviation probabilityasymptoticsLaplace integralquantile estimationvalue at risk

MSC classification

Primary: 60G35: Signal detection and filtering
Secondary: 62E17: Approximations to distributions (nonasymptotic) 62P05: Applications to actuarial sciences and financial mathematics 91B30: Risk theory, insurance

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 2 , June 2005 , pp. 426 - 445
Copyright
© Applied Probability Trust 2005 

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