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Journal of Financial Econometrics Advance Access originally published online on May 25, 2008
Journal of Financial Econometrics 2008 6(3):291-306; doi:10.1093/jjfinec/nbn008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

A Simple Test for GARCH Against a Stochastic Volatility Model

Philip Hans Franses
     Econometric Institute, Erasmus University Rotterdam

Marco van der Leij
     Department of Economics, University of Alicante

Richard Paap
     Econometric Institute, Erasmus University Rotterdam

Address correspondence to Philip Hans Franses, Erasmus University Rotterdam, Econometric Institute H11-34, P. O. Box 1738, NL-3000 DR Rotterdam, The Netherlands, or e-mail: franses{at}few.eur.nl.

JEL Classification: C22, C52


   Abstract

GARCH models and Stochastic Volatility (SV) models can both be used to describe unobserved volatility in asset returns. We consider the issue of testing a GARCH model against an SV model. For that purpose, we propose a new and parsimonious GARCH-t model with an additional restricted moving average term, which can capture SV model properties. We discuss model representation, parameter estimation, and our simple test for model selection. Furthermore, we derive the theoretical moments and the autocorrelation function of our new model. We illustrate our model and test for nine daily stock-return series.

KEYWORDS: GARCH, model selection, stochastic volatility


We thank the associate editor, three anonymous reviewers, and in particular Eric Renault for helpful suggestions. We thank Torben Andersen, Dennis Fok, Jun Wu, Asger Lunde, Peter Boswijk, Marius Ooms, Charles Bos, Michael McAleer, and Robert Engle for their comments made at several seminar presentations.

Received September 6, 2006; revised November 2, 2007; accepted April 10, 2008


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