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The BDS Test as a Test for the Adequacy of a GARCH(1,1) Specification: A Monte Carlo Study

The BDS Test as a Test for the Adequacy of a GARCH(1,1) Specification: A Monte Carlo Study In this study we examine the widely used Brock, Dechert, and Scheinkman (BDS) test when applied to the logarithm of the squared standardized residuals of an estimated GARCH(1,1) model as a test for the adequacy of this specification. We review the conditions derived by De Lima (1996; Econometric Reviews 15, 237–259) for the nuisance-parameter-free property to hold and address the issue of their necessity, using the flexible framework offered by the GARCH(1,1) model in terms of moment, memory, and time heterogeneity properties. By means of Monte Carlo simulations, we show that the BDS test statistic still approximates the standard null distribution even for mildly explosive processes that violate the majority of the conditions. Thus the test performs reasonably well, its empirical size being rather close to the nominal one. As a by-product of this study, we also shed light on the related issue of the consistency of the QML estimators of the conditional variance parameters under various parameter configurations and alternative distributional assumptions on the innovation process. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Financial Econometrics Oxford University Press

The BDS Test as a Test for the Adequacy of a GARCH(1,1) Specification: A Monte Carlo Study

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References (22)

Publisher
Oxford University Press
Copyright
© The Author 2005. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oupjournals.org.
ISSN
1479-8409
eISSN
1479-8417
DOI
10.1093/jjfinec/nbi010
Publisher site
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Abstract

In this study we examine the widely used Brock, Dechert, and Scheinkman (BDS) test when applied to the logarithm of the squared standardized residuals of an estimated GARCH(1,1) model as a test for the adequacy of this specification. We review the conditions derived by De Lima (1996; Econometric Reviews 15, 237–259) for the nuisance-parameter-free property to hold and address the issue of their necessity, using the flexible framework offered by the GARCH(1,1) model in terms of moment, memory, and time heterogeneity properties. By means of Monte Carlo simulations, we show that the BDS test statistic still approximates the standard null distribution even for mildly explosive processes that violate the majority of the conditions. Thus the test performs reasonably well, its empirical size being rather close to the nominal one. As a by-product of this study, we also shed light on the related issue of the consistency of the QML estimators of the conditional variance parameters under various parameter configurations and alternative distributional assumptions on the innovation process.

Journal

Journal of Financial Econometrics – Oxford University Press

Published: Jan 1, 2005

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