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Equivalence Between Out-of-Sample Forecast Comparisons and Wald Statistics

Author

Listed:
  • Peter Reinhard Hansen

    () (European University Institute and CREATES)

  • Allan Timmermann

    () (UCSD and CREATES)

Abstract

We establish the equivalence between a commonly used out-of-sample test of equal predictive accuracy and the difference between two Wald statistics. This equivalence greatly simpli?es the computational burden of calculating recursive out-of-sample tests and evaluating their critical values. Our results shed new light on many aspects of the test and establishes certain weaknesses associated with using out-of-sample forecast comparison tests to conduct inference about nested regression models.

Suggested Citation

  • Peter Reinhard Hansen & Allan Timmermann, 2012. "Equivalence Between Out-of-Sample Forecast Comparisons and Wald Statistics," CREATES Research Papers 2012-45, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2012-45
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    File URL: ftp://ftp.econ.au.dk/creates/rp/12/rp12_45.pdf
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    References listed on IDEAS

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    1. Barbara Rossi & Atsushi Inoue, 2012. "Out-of-Sample Forecast Tests Robust to the Choice of Window Size," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 432-453, April.
    2. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November.
    3. Clark, Todd E. & McCracken, Michael W., 2001. "Tests of equal forecast accuracy and encompassing for nested models," Journal of Econometrics, Elsevier, vol. 105(1), pages 85-110, November.
    4. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-1084, September.
    5. Peter Reinhard Hansen & Allan Timmermann, 2012. "Choice of Sample Split in Out-of-Sample Forecast Evaluation," CREATES Research Papers 2012-43, Department of Economics and Business Economics, Aarhus University.
    6. Todd Clark & Michael McCracken, 2005. "Evaluating Direct Multistep Forecasts," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 369-404.
    7. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
    8. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
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    Cited by:

    1. Daniel Borup & Martin Thyrsgaard, 1705. "Statistical tests for equal predictive ability across multiple forecasting methods," CREATES Research Papers 2017-19, Department of Economics and Business Economics, Aarhus University.
    2. Gonçalves, Sílvia & McCracken, Michael W. & Perron, Benoit, 2017. "Tests of equal accuracy for nested models with estimated factors," Journal of Econometrics, Elsevier, vol. 198(2), pages 231-252.

    More about this item

    Keywords

    Out-of-sample Forecast Evaluation; Nested Models; Testing.;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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