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Using Out-of-Sample Mean Squared Prediction Errors to Test the Martingale Difference

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  • Todd E. Clark
  • Kenneth D. West
Abstract
We consider using out-of-sample mean squared prediction errors (MSPEs) to evaluate the null that a given series follows a zero mean martingale difference against the alternative that it is linearly predictable. Under the null of no predictability, the population MSPE of the null "no change" model equals that of the linear alternative. We show analytically and via simulations that despite this equality, the alternative model's sample MSPE is expected to be greater than the null's. For rolling regression estimators of the alternative model's parameters, we propose and evaluate an asymptotically normal test that properly accounts for the upward shift of the sample MSPE of the alternative model. Our simulations indicate that our proposed procedure works well.

Suggested Citation

  • Todd E. Clark & Kenneth D. West, 2005. "Using Out-of-Sample Mean Squared Prediction Errors to Test the Martingale Difference," NBER Technical Working Papers 0305, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberte:0305
    Note: TWP AP IFM
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    Cited by:

    1. Clark, Todd E. & West, Kenneth D., 2007. "Approximately normal tests for equal predictive accuracy in nested models," Journal of Econometrics, Elsevier, vol. 138(1), pages 291-311, May.
    2. John Y. Campbell & Samuel B. Thompson, 2008. "Predicting Excess Stock Returns Out of Sample: Can Anything Beat the Historical Average?," The Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1509-1531, July.
    3. Lees, Kirdan & Matheson, Troy, 2007. "Mind your ps and qs! Improving ARMA forecasts with RBC priors," Economics Letters, Elsevier, vol. 96(2), pages 275-281, August.
    4. Carstensen Kai & Wohlrabe Klaus & Ziegler Christina, 2011. "Predictive Ability of Business Cycle Indicators under Test: A Case Study for the Euro Area Industrial Production," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 231(1), pages 82-106, February.
    5. 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.
    6. Adriana Fernandez & Evan F. Koenig & Alex Nikolsko-Rzhevskyy, 2011. "A real-time historical database for the OECD," Globalization Institute Working Papers 96, Federal Reserve Bank of Dallas.
    7. West, Kenneth D., 2006. "Forecast Evaluation," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 3, pages 99-134, Elsevier.
    8. Onur Ince & Tanya Molodtsova, 2013. "Real-Time Out-of-Sample Exchange Rate Predictability," Working Papers 13-03, Department of Economics, Appalachian State University.
    9. Jacob Boudoukh & Matthew Richardson & Robert Whitelaw, 2005. "The Information in Long-Maturity Forward Rates: Implications for Exchange Rates and the Forward Premium Anomaly," NBER Working Papers 11840, National Bureau of Economic Research, Inc.

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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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