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A statistical test for forecast evaluation under a discrete loss function

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Abstract

We propose a new approach to evaluating the usefulness of a set of forecasts, based on the use of a discrete loss function de ned on the space of data and forecasts. Existing procedures for such an evaluation either do not allow for formal testing, or use tests statistics based just on the frequency distribution of (data, forecasts) -pairs. They can easily lead to misleading conclusions in some reasonable situations, because of the way they formalize the underlying null hypothesis that "the set of forecasts is not useful". Even though the ambiguity of the underlying null hypothesis precludes us from performing a standard analysis of the size and power of the tests, we get results suggesting that the proposed DISC test performs better than its competitors.

Suggested Citation

  • Francisco J. Eransus & Alfonso Novales Cinca, 2011. "A statistical test for forecast evaluation under a discrete loss function," Documentos de Trabajo del ICAE 2011-07, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
  • Handle: RePEc:ucm:doicae:1107
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    1. Henriksson, Roy D & Merton, Robert C, 1981. "On Market Timing and Investment Performance. II. Statistical Procedures for Evaluating Forecasting Skills," The Journal of Business, University of Chicago Press, vol. 54(4), pages 513-533, October.
    2. Ash, J. C. K. & Smyth, D. J. & Heravi, S. M., 1998. "Are OECD forecasts rational and useful?: a directional analysis," International Journal of Forecasting, Elsevier, vol. 14(3), pages 381-391, September.
    3. Greer, Mark, 2003. "Directional accuracy tests of long-term interest rate forecasts," International Journal of Forecasting, Elsevier, vol. 19(2), pages 291-298.
    4. Pesaran, M Hashem & Timmermann, Allan, 1992. "A Simple Nonparametric Test of Predictive Performance," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(4), pages 561-565, October.
    5. Joutz, Fred & Stekler, H. O., 2000. "An evaluation of the predictions of the Federal Reserve," International Journal of Forecasting, Elsevier, vol. 16(1), pages 17-38.
    6. Merton, Robert C, 1981. "On Market Timing and Investment Performance. I. An Equilibrium Theory of Value for Market Forecasts," The Journal of Business, University of Chicago Press, vol. 54(3), pages 363-406, July.
    7. Mills, Terence C. & Pepper, Gordon T., 1999. "Assessing the forecasters: an analysis of the forecasting records of the Treasury, the London Business School and the National Institute," International Journal of Forecasting, Elsevier, vol. 15(3), pages 247-257, July.
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    Keywords

    Forecasting Evaluation; Loss Function.;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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