The BDS Test as a Test for the Adequacy of a GARCH(1,1) Specification: A Monte Carlo Study
AbstractIn 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. Copyright 2005, Oxford University Press.
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Bibliographic InfoArticle provided by Society for Financial Econometrics in its journal Journal of Financial Econometrics.
Volume (Year): 3 (2005)
Issue (Month): 2 ()
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- Isao Ishida & Toshiaki Watanabe, 2009.
"Modeling and Forecasting the Volatility of the Nikkei 225 Realized Volatility Using the ARFIMA-GARCH Model,"
CIRJE F-Series, CIRJE, Faculty of Economics, University of Tokyo
CIRJE-F-608, CIRJE, Faculty of Economics, University of Tokyo.
- Isao Ishida & Toshiaki Watanabe, 2009. "Modeling and Forecasting the Volatility of the Nikkei 225 Realized Volatility Using the ARFIMA-GARCH Model," Global COE Hi-Stat Discussion Paper Series, Institute of Economic Research, Hitotsubashi University gd08-032, Institute of Economic Research, Hitotsubashi University.
- Isao Ishida & Toshiaki Watanabe, 2009. "Modeling and Forecasting the Volatility of the Nikkei 225 Realized Volatility Using the ARFIMA-GARCH Model," CARF F-Series, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo CARF-F-145, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
- Jorge Pérez-Rodríguez & Julián Andrada-Félix, 2013. "Estimating critical values for testing the i.i.d. in standardized residuals from GARCH models in finite samples," Computational Statistics, Springer, Springer, vol. 28(2), pages 701-734, April.
- Borusyak, K., 2011. "Nonlinear Dynamics of the Russian Stock Market in Problems of Risk Management," Journal of the New Economic Association, New Economic Association, New Economic Association, issue 11, pages 85-105.
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