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Data-Driven Smooth Tests for the Martingale Difference Hypothesis

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  • Juan Carlos Escanciano

    (Indiana University)

  • Silvia Mayoral

    (Universidad de Navarra)

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.

Suggested Citation

  • Juan Carlos Escanciano & Silvia Mayoral, 2007. "Data-Driven Smooth Tests for the Martingale Difference Hypothesis," Faculty Working Papers 01/07, School of Economics and Business Administration, University of Navarra.
  • Handle: RePEc:una:unccee:wp0107
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    References listed on IDEAS

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    1. Deo, Rohit S., 2000. "Spectral tests of the martingale hypothesis under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 99(2), pages 291-315, December.
    2. Escanciano, J. Carlos & Velasco, Carlos, 2006. "Testing the martingale difference hypothesis using integrated regression functions," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2278-2294, December.
    3. Escanciano, J. Carlos, 2009. "On The Lack Of Power Of Omnibus Specification Tests," Econometric Theory, Cambridge University Press, vol. 25(1), pages 162-194, February.
    4. 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.
    5. George Kapetanios & Andrew P. Blake, 2007. "Testing the Martingale Difference Hypothesis Using Neural Network Approximations," Working Papers 601, Queen Mary University of London, School of Economics and Finance.
    6. 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.
    7. Escanciano, J. Carlos & Lobato, Ignacio N., 2009. "An automatic Portmanteau test for serial correlation," Journal of Econometrics, Elsevier, vol. 151(2), pages 140-149, August.
    8. Hervé Cardot & Frédéric Ferraty & André Mas & Pascal Sarda, 2003. "Testing Hypotheses in the Functional Linear Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 241-255, March.
    9. Escanciano, J. Carlos, 2006. "Goodness-of-Fit Tests for Linear and Nonlinear Time Series Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 531-541, June.
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    Cited by:

    1. Teresa Ledwina & Grzegorz Wyłupek, 2012. "Nonparametric tests for stochastic ordering," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 730-756, December.
    2. Zdeněk Hlávka & Marie Hušková & Claudia Kirch & Simos G. Meintanis, 2017. "Fourier--type tests involving martingale difference processes," Econometric Reviews, Taylor & Francis Journals, vol. 36(4), pages 468-492, April.
    3. Escanciano, J. Carlos & Lobato, Ignacio N., 2009. "An automatic Portmanteau test for serial correlation," Journal of Econometrics, Elsevier, vol. 151(2), pages 140-149, August.
    4. Hsu, Shih-Hsun & Kuan, Chung-Ming, 2014. "Constructing smooth tests without estimating the eigenpairs of the limiting process," Journal of Econometrics, Elsevier, vol. 178(P1), pages 71-79.
    5. Junjie Guo & Juan Carlos Escanciano & Jinho Choi, 2017. "Identification and Generalized Band Spectrum Estimation of the New Keynesian Phillips Curve," CAEPR Working Papers 2017-014, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    6. Huang, Henry H. & Wang, Kent & Wang, Zhanglong, 2016. "A test of efficiency for the S&P 500 index option market using the generalized spectrum method," Journal of Banking & Finance, Elsevier, vol. 64(C), pages 52-70.

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