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

Author

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  • 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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    References listed on IDEAS

    as
    1. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
    2. 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.
    3. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November.
    4. 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.
    5. de Jong, Robert M. & Davidson, James, 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals I," Econometric Theory, Cambridge University Press, vol. 16(5), pages 621-642, October.
    6. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-1084, September.
    7. 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.
    8. Todd Clark & Michael McCracken, 2005. "Evaluating Direct Multistep Forecasts," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 369-404.
    9. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(4), pages 489-500, December.
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    Cited by:

    1. 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.
    2. Martin, Ian W.R. & Nagel, Stefan, 2022. "Market efficiency in the age of big data," Journal of Financial Economics, Elsevier, vol. 145(1), pages 154-177.
    3. Allan Timmermann, 2018. "Forecasting Methods in Finance," Annual Review of Financial Economics, Annual Reviews, vol. 10(1), pages 449-479, November.
    4. Daniel Borup & Martin Thyrsgaard, 2017. "Statistical tests for equal predictive ability across multiple forecasting methods," CREATES Research Papers 2017-19, Department of Economics and Business Economics, Aarhus University.
    5. Philippe Goulet Coulombe & Maxime Leroux & Dalibor Stevanovic & Stéphane Surprenant, 2022. "How is machine learning useful for macroeconomic forecasting?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(5), pages 920-964, August.
    6. Firmin Doko Tchatoka & Qazi Haque, 2023. "On bootstrapping tests of equal forecast accuracy for nested models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(7), pages 1844-1864, November.
    7. Rui Liu, 2019. "Forecasting Bond Risk Premia with Unspanned Macroeconomic Information," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 9(01), pages 1-62, March.
    8. Timmermann, Allan & Zhu, Yinchu, 2021. "Conditional Rotation Between Forecasting Models," CEPR Discussion Papers 15917, C.E.P.R. Discussion Papers.
    9. Kothari, Pratik & O’Doherty, Michael S., 2023. "Job postings and aggregate stock returns," Journal of Financial Markets, Elsevier, vol. 64(C).
    10. Knut Are Aastveit & Claudia Foroni & Francesco Ravazzolo, 2017. "Density Forecasts With Midas Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(4), pages 783-801, June.
    11. Wang, Cindy S.H. & Fan, Rui & Xie, Yiqiang, 2023. "Market systemic risk, predictability and macroeconomics news," Finance Research Letters, Elsevier, vol. 56(C).
    12. Jean-Yves Pitarakis, 2020. "A Novel Approach to Predictive Accuracy Testing in Nested Environments," Papers 2008.08387, arXiv.org, revised Oct 2023.
    13. Andrew B. Martinez, 2020. "Extracting Information from Different Expectations," Working Papers 2020-008, The George Washington University, Department of Economics, H. O. Stekler Research Program on Forecasting.
    14. Hunt, Ian, 2022. "In-sample tests of predictability are superior to pseudo-out-of-sample tests, even when data mining," International Journal of Forecasting, Elsevier, vol. 38(3), pages 872-877.
    15. Andrew Martinez, 2017. "Testing for Differences in Path Forecast Accuracy: Forecast-Error Dynamics Matter," Working Papers (Old Series) 1717, Federal Reserve Bank of Cleveland.
    16. Qu, Ritong & Timmermann, Allan & Zhu, Yinchu, 2023. "Comparing forecasting performance in cross-sections," Journal of Econometrics, Elsevier, vol. 237(2).
    17. Christis Katsouris, 2023. "Limit Theory under Network Dependence and Nonstationarity," Papers 2308.01418, arXiv.org, revised Aug 2023.
    18. Timmermann, Allan & Zhu, Yinchu, 2019. "Comparing Forecasting Performance with Panel Data," CEPR Discussion Papers 13746, C.E.P.R. Discussion Papers.
    19. Zhu, Yinchu & Timmermann, Allan, 2022. "Conditional rotation between forecasting models," Journal of Econometrics, Elsevier, vol. 231(2), pages 329-347.
    20. Ciner, Cetin, 2019. "Do industry returns predict the stock market? A reprise using the random forest," The Quarterly Review of Economics and Finance, Elsevier, vol. 72(C), pages 152-158.

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    More about this item

    Keywords

    Out-of-sample Forecast Evaluation; Nested Models; Testing.;
    All these keywords.

    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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