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Testing the Martingale Hypothesis

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  • Peter C. B. Phillips
  • Sainan Jin

Abstract

We propose new tests of the martingale hypothesis based on generalized versions of the Kolmogorov-Smirnov and Cramér-von Mises tests. The tests are distribution-free and allow for a weak drift in the null model. The methods do not require either smoothing parameters or bootstrap resampling for their implementation and so are well suited to practical work. The article develops limit theory for the tests under the null and shows that the tests are consistent against a wide class of nonlinear, nonmartingale processes. Simulations show that the tests have good finite sample properties in comparison with other tests particularly under conditional heteroscedasticity and mildly explosive alternatives. An empirical application to major exchange rate data finds strong evidence in favor of the martingale hypothesis, confirming much earlier research.

Suggested Citation

  • Peter C. B. Phillips & Sainan Jin, 2014. "Testing the Martingale Hypothesis," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 537-554, October.
  • Handle: RePEc:taf:jnlbes:v:32:y:2014:i:4:p:537-554
    DOI: 10.1080/07350015.2014.908780
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    References listed on IDEAS

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    Cited by:

    1. Daniel Borup & Martin Thyrsgaard, 1705. "Statistical tests for equal predictive ability across multiple forecasting methods," CREATES Research Papers 2017-19, Department of Economics and Business Economics, Aarhus University.

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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