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Testing the Martingale Difference Hypothesis Using Neural Network Approximations

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Author Info

  • George Kapetanios

    ()
    (Queen Mary, University of London)

  • Andrew P. Blake

    ()
    (Bank of England)

Abstract

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.

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Bibliographic Info

Paper provided by Queen Mary, University of London, School of Economics and Finance in its series Working Papers with number 601.

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Date of creation: Jun 2007
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Handle: RePEc:qmw:qmwecw:wp601

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Keywords: Martingale difference hypothesis; Neural networks; Boosting;

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References

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  1. 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.
  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. Blake, Andrew P., 2002. "A 'Timeless Perspective' on Optimality in Forward-Looking Rational Expectations Models," Royal Economic Society Annual Conference 2002 30, Royal Economic Society.
  4. 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.
  5. Manuel A. Dominguez & Ignacio N. Lobato, 2001. "A Consistent Test for the Martingale Difference Hypothesis," Working Papers 0101, Centro de Investigacion Economica, ITAM.
  6. 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. Juan Carlos Escanciano & Silvia Mayoral, . "Data-Driven Smooth Tests for the Martingale Difference Hypothesis," Faculty Working Papers 01/07, School of Economics and Business Administration, University of Navarra.

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