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Data-Driven Smooth Tests for the Martingale Difference Hypothesis

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Author Info
Juan Carlos Escanciano () (Indiana University)
Silvia Mayoral () (Universidad de Navarra)

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Abstract

A general method for testing the martingale difference hypothesis is proposed. The new tests are data-driven smooth tests based on the principal components of certain marked empirical processes that are asymptotically distribution-free, with critical values that are already tabulated. The data-driven smooth tests are optimal in a semiparametric sense discussed in the paper, and they are robust to conditional heteroskedasticity of unknown form. A simulation study shows that the smooth tests perform very well for a wide range of realistic alternatives and have more power than the omnibus and other competing tests. Finally, an application to the S&P 500 stock index and some of its components highlights the merits of our approach.

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Paper provided by School of Economics and Business Administration, University of Navarra in its series Faculty Working Papers with number 01/07.

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Handle: RePEc:una:unccee:wp0107

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  1. Miguel A. Delgado & Javier Hidalgo & Carlos Velasco, 2005. "Distribution Free Goodness-of-Fit Tests for Linear Processes," STICERD - Econometrics Paper Series /2005/482, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  2. Hsieh, David A, 1989. "Testing for Nonlinear Dependence in Daily Foreign Exchange Rates," Journal of Business, University of Chicago Press, vol. 62(3), pages 339-68, July. [Downloadable!] (restricted)
  3. Escanciano, J. Carlos & Velasco, Carlos, 2006. "Generalized spectral tests for the martingale difference hypothesis," Journal of Econometrics, Elsevier, vol. 134(1), pages 151-185, September. [Downloadable!] (restricted)
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  4. Juan Carlos Escanciano, 2005. "Goodness-of-fit Tests for Linear and Non-linear Time Series Models," Faculty Working Papers 02/05, School of Economics and Business Administration, University of Navarra. [Downloadable!]
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  5. Fan J. & Huang L-S., 2001. "Goodness-of-Fit Tests for Parametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 640-652, June. [Downloadable!] (restricted)
  6. Stute, W. & Presedo Quindimil, M. & González Manteiga, W. & Koul, H.L., 2006. "Model checks of higher order time series," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1385-1396, July. [Downloadable!] (restricted)
  7. Winfried Stute, 2002. "Model Checks for Generalized Linear Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association and Swedish Statistical Association, vol. 29(3), pages 535-545. [Downloadable!] (restricted)
  8. R. L. Eubank, 2000. "Testing for No Effect by Cosine Series Methods," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association and Swedish Statistical Association, vol. 27(4), pages 747-763. [Downloadable!] (restricted)
  9. Manuel A. Dominguez & Ignacio N. Lobato, 2001. "A Consistent Test for the Martingale Difference Hypothesis," Working Papers 0101, Centro de Investigacion Economica, ITAM. [Downloadable!]
  10. Durlauf, Steven N., 1991. "Spectral based testing of the martingale hypothesis," Journal of Econometrics, Elsevier, vol. 50(3), pages 355-376, December. [Downloadable!] (restricted)
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  11. Juan Carlos Escanciano, 2005. "On the Asymptotic Power Properties of Specification Tests for Dynamic Parametric Regressions," Faculty Working Papers 07/05, School of Economics and Business Administration, University of Navarra. [Downloadable!]
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This page was last updated on 2009-11-19.

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