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A Simple Out-of-Sample Test for the Martingale Difference Hypothesis

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  • Pablo Pincheira

Abstract

We show that a straightforward modification of a trading based test for predictability displays interesting advantages over the Excess Profitability (EP) test proposed by Anatolyev and Gerco when testing the Martingale Difference Hypothesis. Our statistic is called Straightforward Excess Profitability (SEP) and avoids the calculation of a term that under the null of no predictability should be zero, but in practice may be sizable. In addition, our test does not require the strong assumption of independency used to derive the EP test. We claim that dependency is the rule and not the exception. We show via Monte Carlo simulations that the SEP test outperforms the EP test in terms of size and power. Finally, we illustrate the use of these tests in an empirical application within the context of the exchange rate literature.

Suggested Citation

  • Pablo Pincheira, 2013. "A Simple Out-of-Sample Test for the Martingale Difference Hypothesis," Working Papers Central Bank of Chile 698, Central Bank of Chile.
    • Handle: RePEc:chb:bcchwp:698
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    References listed on IDEAS

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    1. Cheung, Yin-Wong & Chinn, Menzie D. & Pascual, Antonio Garcia, 2005. "Empirical exchange rate models of the nineties: Are any fit to survive?," Journal of International Money and Finance, Elsevier, vol. 24(7), pages 1150-1175, November.
    2. Pablo Matias Pincheira Brown, 2013. "Shrinkage‐Based Tests of Predictability," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(4), pages 307-332, July.
    3. Atsushi Inoue & Lutz Kilian, 2005. "In-Sample or Out-of-Sample Tests of Predictability: Which One Should We Use?," Econometric Reviews, Taylor & Francis Journals, vol. 23(4), pages 371-402.
    4. Meese, Richard A. & Rogoff, Kenneth, 1983. "Empirical exchange rate models of the seventies : Do they fit out of sample?," Journal of International Economics, Elsevier, vol. 14(1-2), pages 3-24, February.
    5. Chao, John & Corradi, Valentina & Swanson, Norman R., 2001. "Out-Of-Sample Tests For Granger Causality," Macroeconomic Dynamics, Cambridge University Press, vol. 5(4), pages 598-620, September.
    6. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
    7. Anatolyev, Stanislav & Gerko, Alexander, 2005. "A Trading Approach to Testing for Predictability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 455-461, October.
    8. Chinn, Menzie D. & Meese, Richard A., 1995. "Banking on currency forecasts: How predictable is change in money?," Journal of International Economics, Elsevier, vol. 38(1-2), pages 161-178, February.
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