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Comptes Rendus Mathématique
Volume 351, n° 5-6
pages 235-239 (mars 2013)
Doi : 10.1016/j.crma.2013.02.014
Received : 25 June 2012 ;  accepted : 27 February 2013
A new nonlinear formulation for GARCH models
Une nouvelle formulation non linéaire pour des modèles GARCH
 

Sebastian Ossandón a , Natalia Bahamonde b
a Instituto de Matemáticas, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso, Chile 
b Instituto de Estadística, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso, Chile 

Abstract

In this note we deduce a new mathematical representation, based on a discrete-time nonlinear state–space formulation, to characterize Generalized AutoRegresive Conditional Heteroskedasticity (GARCH) models. The purpose pursued by this article is to use the models presented herein to develop estimation techniques which are also valid in the situation when observations are missing.

The full text of this article is available in PDF format.
Résumé

Dans cette note, on déduit une nouvelle représentation mathématique, basée sur une formulation espace–état en temps discret non linéaire, pour caractériser le modèle GARCH. Lʼobjectif poursuivi dans ce travail est dʼutiliser les modèles présentés ici afin de développer des techniques dʼestimation qui soient aussi valables dans des situations où des données sont manquantes.

The full text of this article is available in PDF format.


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