[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/aah/create/2012-45.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: https://repec.econ.au.dk/repec/creates/rp/12/rp12_45.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Clark, Todd & McCracken, Michael, 2013. "Advances in Forecast Evaluation," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1107-1201, Elsevier.
    2. 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.
    3. 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.
    4. 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.
    5. Rossi, Barbara, 2013. "Advances in Forecasting under Instability," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1203-1324, Elsevier.
    6. Todd E. Clark & Michael W. Mccracken, 2014. "Tests Of Equal Forecast Accuracy For Overlapping Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(3), pages 415-430, April.
    7. Clark, Todd E. & McCracken, Michael W., 2015. "Nested forecast model comparisons: A new approach to testing equal accuracy," Journal of Econometrics, Elsevier, vol. 186(1), pages 160-177.
    8. Richard A. Ashley & Kwok Ping Tsang, 2014. "Credible Granger-Causality Inference with Modest Sample Lengths: A Cross-Sample Validation Approach," Econometrics, MDPI, vol. 2(1), pages 1-20, March.
    9. Todd E. Clark & Michael W. McCracken, 2010. "Reality checks and nested forecast model comparisons," Working Papers 2010-032, Federal Reserve Bank of St. Louis.
    10. Brooks, Chris & Burke, Simon P. & Stanescu, Silvia, 2016. "Finite sample weighting of recursive forecast errors," International Journal of Forecasting, Elsevier, vol. 32(2), pages 458-474.
    11. Mogliani, Matteo & Darné, Olivier & Pluyaud, Bertrand, 2017. "The new MIBA model: Real-time nowcasting of French GDP using the Banque de France's monthly business survey," Economic Modelling, Elsevier, vol. 64(C), pages 26-39.
    12. Pablo Pincheira Brown, 2022. "A Power Booster Factor for Out-of-Sample Tests of Predictability," Revista Economía, Fondo Editorial - Pontificia Universidad Católica del Perú, vol. 45(89), pages 150-183.
    13. Todd E. Clark & Michael W. McCracken, 2009. "Combining Forecasts from Nested Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(3), pages 303-329, June.
    14. Ferrara, Laurent & Marcellino, Massimiliano & Mogliani, Matteo, 2015. "Macroeconomic forecasting during the Great Recession: The return of non-linearity?," International Journal of Forecasting, Elsevier, vol. 31(3), pages 664-679.
    15. Granziera, Eleonora & Hubrich, Kirstin & Moon, Hyungsik Roger, 2014. "A predictability test for a small number of nested models," Journal of Econometrics, Elsevier, vol. 182(1), pages 174-185.
    16. 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.
    17. Jean-Yves Pitarakis, 2020. "A Novel Approach to Predictive Accuracy Testing in Nested Environments," Papers 2008.08387, arXiv.org, revised Oct 2023.
    18. Kirstin Hubrich & Kenneth D. West, 2010. "Forecast evaluation of small nested model sets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 574-594.
    19. Thomadakis, Apostolos, 2016. "Do Combination Forecasts Outperform the Historical Average? Economic and Statistical Evidence," MPRA Paper 71589, University Library of Munich, Germany.
    20. Norman Swanson & Nii Ayi Armah, 2006. "Predictive Inference Under Model Misspecification with an Application to Assessing the Marginal Predictive Content of Money for Output," Departmental Working Papers 200619, Rutgers University, Department of Economics.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:aah:create:2012-45. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: http://www.econ.au.dk/afn/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.