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Testing the Martingale Difference Hypothesis Using Neural Network Approximations


  • George Kapetanios

    () (Queen Mary, University of London)

  • Andrew P. Blake

    () (Bank of England)


The martingale difference restriction is an outcome of many theoretical analyses in economics and finance. A large body of econometric literature deals with tests of that restriction. We provide new tests based on radial basis function neural networks. Our work is based on the test design of Blake and Kapetanios (2000, 2003a,b). However, unlike that work we can provide a formal theoretical justification for the validity of these tests using approximation results from Kapetanios and Blake (2007). These results take advantage of the link between the algorithms of Blake and Kapetanios (2000, 2003a,b) and boosting. We carry out a Monte Carlo study of the properties of the new tests and find that they have superior power performance to all existing tests of the martingale difference hypothesis we consider. An empirical application to the S&P500 constituents illustrates the usefulness of our new test.

Suggested Citation

  • 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.
  • Handle: RePEc:qmw:qmwecw:wp601

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    References listed on IDEAS

    1. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June.
    2. George Kapetanios & Andrew P. Blake, 2007. "Boosting Estimation of RBF Neural Networks for Dependent Data," Working Papers 588, Queen Mary University of London, School of Economics and Finance.
    3. Andrew Blake, 2001. "A Timeless Perspective on Optimality in Forward-Looking Rational Expectations Models," National Institute of Economic and Social Research (NIESR) Discussion Papers 188, National Institute of Economic and Social Research.
    4. Manuel A. Dominguez & Ignacio N. Lobato, 2001. "A Consistent Test for the Martingale Difference Hypothesis," Working Papers 0101, Centro de Investigacion Economica, ITAM.
    5. Guay, Alain & Guerre, Emmanuel, 2006. "A Data-Driven Nonparametric Specification Test For Dynamic Regression Models," Econometric Theory, Cambridge University Press, vol. 22(04), pages 543-586, August.
    6. de Jong, Robert M., 1996. "The Bierens test under data dependence," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 1-32.
    7. D. S. Poskitt, 2005. "Autoregressive Approximation in Nonstandard Situations: The Non-Invertible and Fractionally Integrated Cases," Monash Econometrics and Business Statistics Working Papers 16/05, Monash University, Department of Econometrics and Business Statistics.
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    Cited by:

    1. Escanciano, Juan Carlos & Mayoral, Silvia, 2010. "Data-driven smooth tests for the martingale difference hypothesis," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1983-1998, August.

    More about this item


    Martingale difference hypothesis; Neural networks; Boosting;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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