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The finite-sample size of the BDS test for GARCH standardized residuals

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  • Fernandes, Marcelo
  • Preumont, Pierre-Yves

Abstract

This paper uses a multivariate response surface methodology to analyze the size distortion of the BDS test when applied to standardized residuals of rst-order GARCH processes. The results show that the asymptotic standard normal distribution is an unreliable approximation, even in large samples. On the other hand, a simple log-transformation of the squared standardized residuals seems to correct most of the size problems. Nonethe-less, the estimated response surfaces can provide not only a measure of the size distortion, but also more adequate critical values for the BDS test in small samples.

Suggested Citation

  • Fernandes, Marcelo & Preumont, Pierre-Yves, 2014. "The finite-sample size of the BDS test for GARCH standardized residuals," Textos para discussão 361, FGV EESP - Escola de Economia de São Paulo, Fundação Getulio Vargas (Brazil).
    • Handle: RePEc:fgv:eesptd:361
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    References listed on IDEAS

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    1. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    2. Chappell, David & Padmore, Joanne & Ellis, Catherine, 1996. "A Note on the Distribution of BDS Statistics for a Real Exchange Rate Series," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(3), pages 561-565, August.
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    Cited by:

    1. Xin Huang & Han Lin Shang & David Pitt, 2022. "A model sufficiency test using permutation entropy," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(5), pages 1017-1036, August.
    2. Luo, Wenya & Bai, Zhidong & Zheng, Shurong & Hui, Yongchang, 2020. "A modified BDS test," Statistics & Probability Letters, Elsevier, vol. 164(C).

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