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The Bds Test As A Test For The Adequacy Of A Garch(1,1) Specification: A Monte Carlo Study

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  • Guglielmo Maria Caporale

    ()

  • Christos Ntantamis
  • Theologos Pantelidis
  • Nikitas Pittis

Abstract

In this study we examine the widely used Brock, Dechert and Scheinkman (BDS) test when applied to the logarithm of the 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 consistency of the QML estimators of the conditional variance parameters under various parameter configurations and alternative distributional assumptions on the innovation process.

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Bibliographic Info

Paper provided by Economics and Finance Section, School of Social Sciences, Brunel University in its series Public Policy Discussion Papers with number 04-14.

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Length: 22 pages
Date of creation: Oct 2004
Date of revision:
Handle: RePEc:bru:bruppp:04-14

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Postal: Brunel University, Uxbridge, Middlesex UB8 3PH, UK

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  1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  2. Davidson, James, 2002. "Establishing conditions for the functional central limit theorem in nonlinear and semiparametric time series processes," Journal of Econometrics, Elsevier, vol. 106(2), pages 243-269, February.
  3. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-96, May.
  4. Shiqing Ling & Michael McAleer, 2001. "Necessary and Sufficient Moment Conditions for the GARCH(r,s) and Asymmetric Power GARCH(r,s) Models," ISER Discussion Paper 0534, Institute of Social and Economic Research, Osaka University.
  5. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(01), pages 29-52, March.
  6. Tim Bollerslev & Jeffrey M. Wooldridge, 1988. "Quasi-Maximum Likelihood Estimation of Dynamic Models with Time-Varying Covariances," Working papers 505, Massachusetts Institute of Technology (MIT), Department of Economics.
  7. He, Changli & Ter svirta, Timo, 1999. "FOURTH MOMENT STRUCTURE OF THE GARCH(p,q) PROCESS," Econometric Theory, Cambridge University Press, vol. 15(06), pages 824-846, December.
  8. Søren Tolver Jensen & Anders Rahbek, 2004. "Asymptotic Normality of the QMLE Estimator of ARCH in the Nonstationary Case," Econometrica, Econometric Society, vol. 72(2), pages 641-646, 03.
  9. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
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Cited by:
  1. Halil Guler & Anil Talasli, 2010. "Modelling the Daily Currency in Circulation in Turkey," Central Bank Review, Research and Monetary Policy Department, Central Bank of the Republic of Turkey, vol. 10(1), pages 29-46.
  2. 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-F-608, CIRJE, Faculty of Economics, University of Tokyo.
  3. Borusyak, K., 2011. "Nonlinear Dynamics of the Russian Stock Market in Problems of Risk Management," Journal of the New Economic Association, New Economic Association, issue 11, pages 85-105.
  4. 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, vol. 28(2), pages 701-734, April.

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