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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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Author Info
Caporale, Guglielmo Maria (London South Bank University)
Ntantamis, Christos (University of Piraeus)
Pantelidis, Theologos (University of Piraeus)
Pittis, Nikitas (University of Piraeus)

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Abstract

In this study, we examine the Brock, Dechert and Scheinkman (BDS) test when applied to the standardised 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 GARCH(1,1) model. By means of Monte Carlo simulations, we show that, provided that the unconditional mean exists, the BDS test statistic still approximates the standard null distribution even when the majority of the conditions are violated. Further, the test performs reasonably well, as its empirical size is rather close to the nominal one. As a by-product of this study, we also examine 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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File URL: http://www.ihs.ac.at/publications/eco/es-156.pdf
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Publisher Info
Paper provided by Institute for Advanced Studies in its series Economics Series with number 156.

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Length: 24 pages
Date of creation: May 2004
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Handle: RePEc:ihs:ihsesp:156

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Related research
Keywords: BDS Test; Nuisance-Parameter Free Property; Monte Carlo Analysis; GARCH(1; 1) Model; QML estimator;

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Find related papers by JEL classification:
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

References listed on IDEAS
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  1. Ling, Shiqing & McAleer, Michael, 2002. "NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS," Econometric Theory, Cambridge University Press, vol. 18(03), pages 722-729, June. [Downloadable!]
    Other versions:
  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. [Downloadable!] (restricted)
  3. Brooks, Chris & Henry, Olan T., 2000. "Can portmanteau nonlinearity tests serve as general mis-specification tests?: Evidence from symmetric and asymmetric GARCH models," Economics Letters, Elsevier, vol. 67(3), pages 245-251, June. [Downloadable!] (restricted)
    Other versions:
  4. Tim Bollerslev & Jeffrey Wooldridge, 1992. "Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances," Econometric Reviews, Taylor and Francis Journals, vol. 11(2), pages 143-172. [Downloadable!] (restricted)
  5. 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. [Downloadable!]
  6. 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. [Downloadable!]
  7. 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.
  8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  9. repec:cup:etheor:v:7:y:1991:i:2:p:213-21 is not listed on IDEAS
  10. Hansen, Bruce E., 1991. "Strong Laws for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 7(02), pages 213-221, June. [Downloadable!]
  11. Brooks, Chris & Heravi, Saeed M, 1999. "The Effect of (Mis-Specified) GARCH Filters on the Finite Sample Distribution of the BDS Test," Computational Economics, Springer, vol. 13(2), pages 147-62, April. [Downloadable!]
  12. Pedro de Lima, 1996. "Nuisance parameter free properties of correlation integral based statistics," Econometric Reviews, Taylor and Francis Journals, vol. 15(3), pages 237-259. [Downloadable!] (restricted)
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