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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. The estimated response surfaces can nonetheless provide not only a measure of the size distortion, but also more adequate critical values for theBDS test in small samples.

Suggested Citation

  • Fernandes, Marcelo & Preumont, Pierre-Yves, 2012. "The Finite-Sample Size of the BDS Test for GARCH Standardized Residuals," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 32(2), April.
    • Handle: RePEc:sbe:breart:v:32:y:2012:i:2:a:18608
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    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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