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Shrinkage Based Tests of the Martingale Difference Hypothesis


  • Pablo Pincheira


In this paper we define a family of tests for the Martingale Difference Hypothesis (MDH) based upon a shrinkage principle. Tests within this family are such that rejection of the null implies that forecasts from the alternative model, adjusted by a shrinkage factor, will display lower Mean Square Prediction Error (MSPE) than forecasts from the null model. This generalizes most previous tests which compare forecast errors of one model, the null, to errors of the plain alternative model, not allowing for shrinkage. We argue that tests derived from this shrinkage approach display in general better small sample properties than MSPE based tests of the MDH. This occurs because the shrinkage based tests implicitly consider the reduced variance benefits of shrinkage estimators. Finally, we illustrate the use of our tests in an empirical application within the exchange rate literature

Suggested Citation

  • Pablo Pincheira, 2006. "Shrinkage Based Tests of the Martingale Difference Hypothesis," Working Papers Central Bank of Chile 376, Central Bank of Chile.
  • Handle: RePEc:chb:bcchwp:376

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    References listed on IDEAS

    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. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-1084, September.
    3. Clemen, Robert T., 1989. "Combining forecasts: A review and annotated bibliography," International Journal of Forecasting, Elsevier, vol. 5(4), pages 559-583.
    4. Skouras, Spyros, 2001. "Financial returns and efficiency as seen by an artificial technical analyst," Journal of Economic Dynamics and Control, Elsevier, vol. 25(1-2), pages 213-244, January.
    5. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    6. Miller, Don M. & Williams, Dan, 2003. "Shrinkage estimators of time series seasonal factors and their effect on forecasting accuracy," International Journal of Forecasting, Elsevier, vol. 19(4), pages 669-684.
    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. Avramov, Doron, 2002. "Stock return predictability and model uncertainty," Journal of Financial Economics, Elsevier, vol. 64(3), pages 423-458, June.
    9. 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.
    10. Norman R. Swanson, 2000. "An Out of Sample Test for Granger Causality," Econometric Society World Congress 2000 Contributed Papers 0362, Econometric Society.
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    Cited by:

    1. Pablo Pincheira, 2008. "Combining Tests of Predictive Ability Theory and Evidence for Chilean and Canadian Exchange Rates," Working Papers Central Bank of Chile 459, Central Bank of Chile.
    2. Ana María Abarca G. & Felipe Alarcón G. & Pablo Pincheira B. & Jorge Selaive C., 2007. "Nominal Exchange Rate in Chile: Predictions based on technical analysis," Journal Economía Chilena (The Chilean Economy), Central Bank of Chile, vol. 10(2), pages 57-80, August.
    3. Pablo Pincheira B., 2007. "Hidden Predictability in Economics: The Case of the Chilean Exchange Rate," Working Papers Central Bank of Chile 435, Central Bank of Chile.
    4. Pablo Pincheira B., 2008. "Predictibilidad Encubierta en Economía: El Caso del Tipo de Cambio Nominal Chileno," Notas de Investigación Journal Economía Chilena (The Chilean Economy), Central Bank of Chile, vol. 11(1), pages 137-142, April.
    5. Pablo Pincheira & Jorge Selaive, 2011. "External imbalance, valuation adjustments and real Exchange rate: evidence of predictability in an emerging economy," Revista de Analisis Economico – Economic Analysis Review, Ilades-Georgetown University, Universidad Alberto Hurtado/School of Economics and Bussines, vol. 26(1), pages 107-125, Junio.
    6. Ana María Abarca & Felipe Alarcón & Pablo Pincheira & Jorge Selaive, 2007. "Chilean Nominal Exchange Rate: Forecasting Based Upon Technical Analysis," Working Papers Central Bank of Chile 425, Central Bank of Chile.
    7. Pablo Pincheira, 2012. "A Joint Test of Superior Predictive Ability for Chilean Inflation Forecasts," Journal Economía Chilena (The Chilean Economy), Central Bank of Chile, vol. 15(3), pages 04-39, December.

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