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A Consistent Test for the Martingale Difference Hypothesis

  • Manuel A. Dominguez
  • Ignacio N. Lobato


    (Centro de Investigacion Economica (CIE), Instituto Tecnologico Autonomo de Mexico (ITAM))

This paper considers testing that an economic time series follows a martingale difference process. The martingale difference hypothesis has been typically tested using information contained in the second moments of a process, that is, using test statistics based on the sample autocovariances or in the periodograms. Tests based on these statistics are inconsistent since they just test necessary conditions of the null hypothesis. In this paper we consider tests that are consistent against all fixed alternatives and against Pitman's local alternatives. Since the asymptotic distributions of the tests statistics depend on the data generating process, the tests are implemented using a modification of the wild bootstrap procedure. The paper justifies theoretically the proposed tests and examines their finite sample behavior by means of Monte Carlo experiments. In addition we include an application to exchange rate data.

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Paper provided by Centro de Investigacion Economica, ITAM in its series Working Papers with number 0101.

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Length: 27 pages
Date of creation: Jan 2001
Date of revision:
Handle: RePEc:cie:wpaper:0101
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  1. Donald W.K. Andrews, 1996. "A Conditional Kolmogorov Test," Cowles Foundation Discussion Papers 1111R, Cowles Foundation for Research in Economics, Yale University.
  2. Bierens, H.J., 1989. "A consistent conditional moment test of functional form," Serie Research Memoranda 0064, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  3. Brooks, Chris & Hinich, Melvin J., 1999. "Cross-correlations and cross-bicorrelations in Sterling exchange rates," Journal of Empirical Finance, Elsevier, vol. 6(4), pages 385-404, October.
  4. 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.
  5. E. Guerre & Pascal Lavergne, 2000. "Minimax Rates for Nonparametric Specification Testing in Regression Models," Econometric Society World Congress 2000 Contributed Papers 0644, Econometric Society.
  6. Bera, Anil K & Higgins, Matthew L, 1997. "ARCH and Bilinearity as Competing Models for Nonlinear Dependence," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 43-50, January.
  7. Hall, Robert E, 1978. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 971-87, December.
  8. de Jong, Robert M., 1996. "The Bierens test under data dependence," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 1-32.
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