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

Posted: 29 Feb 2008

See all articles by Guglielmo Maria Caporale

Guglielmo Maria Caporale

Brunel University London - Department of Economics and Finance; London South Bank University; CESifo (Center for Economic Studies and Ifo Institute); German Institute for Economic Research (DIW Berlin)

Christos Ntantamis

Dalhousie University - Department of Economics; Mount Allison University - Department of Economics

Theologos Pantelidis

University of Kent

Nikitas Pittis

University of Piraeus - Department of Banking and Financial Management

Date Written: 2005

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.

Keywords: BDS test, GARCH(1,1) model, nuisance-parameter free property, QML estimator

Suggested Citation

Caporale, Guglielmo Maria and Ntantamis, Christos and Pantelidis, Theologos and Pittis, Nikitas, The Bds Test as a Test for the Adequacy of a Garch(1,1) Specification: A Monte Carlo Study ( 2005). Journal of Financial Econometrics, Vol. 3, No. 2, pp. 282-309, Spring 2005, Available at SSRN: https://ssrn.com/abstract=821745

Guglielmo Maria Caporale (Contact Author)

Brunel University London - Department of Economics and Finance ( email )

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Marie Jahoda Building
Uxbridge, Middlesex UB8 3PH
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+44 1895 269770 (Fax)

HOME PAGE: http://www.brunel.ac.uk/about/acad/bbs/bbsstaff/ef_staff/guglielmocaporale/

London South Bank University ( email )

Centre for Monetary and Financial Economics
London
United Kingdom

CESifo (Center for Economic Studies and Ifo Institute)

Poschinger Str. 5
Munich, DE-81679
Germany

German Institute for Economic Research (DIW Berlin) ( email )

Mohrenstra├če 58
Berlin, 10117
Germany

Christos Ntantamis

Dalhousie University - Department of Economics ( email )

Halifax, Nova Scotia B3H 3J5
Canada

Mount Allison University - Department of Economics ( email )

144 Main Street
Sackville, New Brunswick E4L1L7
Canada

Theologos Pantelidis

University of Kent ( email )

Canterbury, Kent CT2 7PE
United Kingdom

Nikitas Pittis

University of Piraeus - Department of Banking and Financial Management ( email )

80 Karaoli & Dimitriou Str.
18534 Piraeus, 185 34 -GR
Greece

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