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A modified BDS test

Author

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  • Luo, Wenya
  • Bai, Zhidong
  • Zheng, Shurong
  • Hui, Yongchang

Abstract

The BDS test is a test for detecting whether a random sequence is i.i.d. (independent and identically distributed). It has been used in economics and finance to examine whether a fitted time series model is adequate by examining whether the residual sequence is nearly i.i.d. Though the BDS test is widely used in the literature, it has a weakness of over-rejecting the null hypothesis even though the sample size T is as large as (100,1000). In this study, we propose a modified BDS test (MBDS test) by removing some terms from the correlation integral, which is the foundation of the BDS test. Theoretical calculations and simulation results show that the MBDS test efficiently corrects the bias of the BDS test.

Suggested Citation

  • Luo, Wenya & Bai, Zhidong & Zheng, Shurong & Hui, Yongchang, 2020. "A modified BDS test," Statistics & Probability Letters, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:stapro:v:164:y:2020:i:c:s0167715220300973
    DOI: 10.1016/j.spl.2020.108794
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    References listed on IDEAS

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    1. M. Matilla-Garcia & P. Sanz & F. J. Vazquez, 2004. "Dimension estimation with the BDS-G statistic," Applied Economics, Taylor & Francis Journals, vol. 36(11), pages 1219-1223.
    2. Genest, Christian & Ghoudi, Kilani & Remillard, Bruno, 2007. "Rank-Based Extensions of the Brock, Dechert, and Scheinkman Test," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1363-1376, December.
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    4. Evzen Kocenda & Lubos Briatka, 2005. "Optimal Range for the iid Test Based on Integration Across the Correlation Integral," Econometric Reviews, Taylor & Francis Journals, vol. 24(3), pages 265-296.
    5. 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.
    6. Guglielmo Maria Caporale, 2005. "The BDS Test as a Test for the Adequacy of a GARCH(1,1) Specification: A Monte Carlo Study," Journal of Financial Econometrics, Oxford University Press, vol. 3(2), pages 282-309.
    7. LeBaron Blake, 1997. "A Fast Algorithm for the BDS Statistic," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 2(2), pages 1-9, July.
    8. Evzen Kocenda, 2001. "An Alternative To The Bds Test: Integration Across The Correlation Integral," Econometric Reviews, Taylor & Francis Journals, vol. 20(3), pages 337-351.
    9. Diks, Cees, 2003. "Detecting serial dependence in tail events: a test dual to the BDS test," Economics Letters, Elsevier, vol. 79(3), pages 319-324, June.
    10. Madhavan, Vinodh, 2013. "Nonlinearity in investment grade Credit Default Swap (CDS) Indices of US and Europe: Evidence from BDS and close-returns tests," Global Finance Journal, Elsevier, vol. 24(3), pages 266-279.
    11. Jorge Belaire-Franch & Dulce Contreras, 2002. "How to compute the BDS test: a software comparison," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(6), pages 691-699.
    12. Matilla-García, Mariano & Marín, Manuel Ruiz, 2010. "A new test for chaos and determinism based on symbolic dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 600-614, December.
    13. 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;Society for Computational Economics, vol. 13(2), pages 147-162, April.
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