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Shrinkage Based Tests of the Martingale Difference Hypothesis

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Pablo Pincheira

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Abstract

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

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Paper provided by Central Bank of Chile in its series Working Papers Central Bank of Chile with number 376.

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Date of creation: Nov 2006
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Handle: RePEc:chb:bcchwp:376

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Todd E. Clark & Michael W. McCracken, 2001. "Evaluating long-horizon forecasts," Research Working Paper RWP 01-14, Federal Reserve Bank of Kansas City. [Downloadable!]
  2. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. repec:att:wimass:1920114 is not listed on IDEAS
  5. Donald J. Brown & Rustam Ibragimov, 2005. "Sign Tests for Dependent Observations and Bounds for Path-Dependent Options," Cowles Foundation Discussion Papers 1518, Cowles Foundation, Yale University. [Downloadable!]
  6. Raffaella Giacomini & Halbert White, 2003. "Tests of Conditional Predictive Ability," Econometrics 0308001, EconWPA. [Downloadable!]
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  7. Patton, Andrew J & Timmermann, Allan G, 2003. "Properties of Optimal Forecasts," CEPR Discussion Papers 4037, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  8. 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. [Downloadable!] (restricted)
  9. West, Kenneth D., 2006. "Forecast Evaluation," Handbook of Economic Forecasting, Elsevier. [Downloadable!] (restricted)
  10. Todd E. Clark & Kenneth D. West, 2005. "Approximately normal tests for equal predictive accuracy in nested models," Research Working Paper RWP 05-05, Federal Reserve Bank of Kansas City. [Downloadable!]
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  11. Lutz Kilian & Atsushi Inoue, 2002. "In-Sample or out-of-sample tests of predictability: which one should we use?," Working Paper Series 195, European Central Bank. [Downloadable!]
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  12. Yin-Wong Cheung & Menzie D. Chinn & Antonio Garcia Pascual, 2002. "Empirical Exchange Rate Models of the Nineties: Are Any Fit to Survive?," NBER Working Papers 9393, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  13. Clark, Todd E. & West, Kenneth D., 2006. "Using out-of-sample mean squared prediction errors to test the martingale difference hypothesis," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 155-186. [Downloadable!] (restricted)
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  14. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-84, September. [Downloadable!] (restricted)
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  15. Jonathan H. Wright, 2003. "Bayesian Model Averaging and exchange rate forecasts," International Finance Discussion Papers 779, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
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  16. 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. [Downloadable!] (restricted)
  17. Clemen, Robert T., 1989. "Combining forecasts: A review and annotated bibliography," International Journal of Forecasting, Elsevier, vol. 5(4), pages 559-583. [Downloadable!] (restricted)
  18. 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. [Downloadable!] (restricted)
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  19. Norman R. Swanson, 2000. "An Out of Sample Test for Granger Causality," Econometric Society World Congress 2000 Contributed Papers 0362, Econometric Society. [Downloadable!]
  20. Avramov, Doron, 2002. "Stock return predictability and model uncertainty," Journal of Financial Economics, Elsevier, vol. 64(3), pages 423-458, June. [Downloadable!] (restricted)
  21. Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-63, July.
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!]
  2. 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. [Downloadable!]
  3. 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. [Downloadable!]
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