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Testing for Symmetry and Conditional Symmetry Using Asymmetric Kernels

Listed author(s):
  • Marcelo FERNANDES

    (University of London)

  • Eduardo F. MENDES

    (Northwestern University)

  • Olivier SCAILLET

    (University of Geneva and Swiss Finance Institute)

We derive nonparametric tests of symmetry using asymmetric kernels with either shrinking or fixed bandwidths. We show how to extend the approach to examine conditional symmetry by deriving conditions under which our tests are applicable to residuals from semiparametric models with a (sufficiently smooth) nonparametric link function. As a by-product, we prove the consistency of the asymmetric kernel estimator of the derivative of the density function. Simulations show that the asymptotic tests perform well even in very small samples, entailing better size and power properties than some of the existing symmetry tests.

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Paper provided by Swiss Finance Institute in its series Swiss Finance Institute Research Paper Series with number 11-32.

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Length: 31 pages
Date of creation:
Handle: RePEc:chf:rpseri:rp1132
Contact details of provider: Web page: http://www.SwissFinanceInstitute.ch

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  4. Gouriéroux, Christian & Laurent, J.P. & Scaillet, Olivier, 1999. "Sensitivity Analysis of Values at Risk," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2000002, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES), revised 00 Jan 2000.
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  6. Fernandes, Marcelo & Grammig, Joachim, 2005. "Nonparametric specification tests for conditional duration models," Journal of Econometrics, Elsevier, vol. 127(1), pages 35-68, July.
  7. Gustafsson, J. & Hagmann, M. & Nielsen, J. P. & Scaillet, O., 2009. "Local Transformation Kernel Density Estimation of Loss Distributions," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 161-175.
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  10. Bai, Jushan & Ng, Serena, 2001. "A consistent test for conditional symmetry in time series models," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 225-258, July.
  11. Lambert, Philippe & Laurent, Sébastien & Veredas, David, 2012. "Testing conditional asymmetry: A residual-based approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(8), pages 1229-1247.
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  13. Bouezmarni, Taoufik & Scaillet, Olivier, 2005. "Consistency Of Asymmetric Kernel Density Estimators And Smoothed Histograms With Application To Income Data," Econometric Theory, Cambridge University Press, vol. 21(02), pages 390-412, April.
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  15. McDonald, James B. & Newey, Whitney K., 1988. "Partially Adaptive Estimation of Regression Models via the Generalized T Distribution," Econometric Theory, Cambridge University Press, vol. 4(03), pages 428-457, December.
  16. Anderson, N. H. & Hall, P. & Titterington, D. M., 1994. "Two-Sample Test Statistics for Measuring Discrepancies Between Two Multivariate Probability Density Functions Using Kernel-Based Density Estimates," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 41-54, July.
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  18. Scaillet, Olivier, 2007. "Kernel-based goodness-of-fit tests for copulas with fixed smoothing parameters," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 533-543, March.
  19. Delgado, Miguel A. & Carlos Escanciano, J., 2007. "Nonparametric tests for conditional symmetry in dynamic models," Journal of Econometrics, Elsevier, vol. 141(2), pages 652-682, December.
  20. Zheng, John Xu, 1998. "Consistent Specification Testing For Conditional Symmetry," Econometric Theory, Cambridge University Press, vol. 14(01), pages 139-149, February.
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