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Diverging Tests of Equal Predictive Ability

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Abstract

We investigate claims made in Giacomini and White (2006) and Diebold (2015) regarding the asymptotic normality of a test of equal predictive ability. A counterexample is provided in which, instead, the test statistic diverges with probability one under the null.

Suggested Citation

  • Michael W. McCracken, 2019. "Diverging Tests of Equal Predictive Ability," Working Papers 2019-018, Federal Reserve Bank of St. Louis, revised 09 Mar 2020.
    • Handle: RePEc:fip:fedlwp:2019-018
    DOI: 10.20955/wp.2019.018
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    1. Giacomini, Raffaella & Komunjer, Ivana, 2005. "Evaluation and Combination of Conditional Quantile Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 416-431, October.
    2. 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.
    3. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    4. Rossi, Barbara & Sekhposyan, Tatevik, 2019. "Alternative tests for correct specification of conditional predictive densities," Journal of Econometrics, Elsevier, vol. 208(2), pages 638-657.
    5. Francis X. Diebold, 2015. "Comparing Predictive Accuracy, Twenty Years Later: A Personal Perspective on the Use and Abuse of Diebold-Mariano Tests," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 1-1, January.
    6. Amisano, Gianni & Giacomini, Raffaella, 2007. "Comparing Density Forecasts via Weighted Likelihood Ratio Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 177-190, April.
    7. 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.
    8. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-161, January.
    9. Raffaella Giacomini & Barbara Rossi, 2010. "Forecast comparisons in unstable environments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 595-620.
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    Cited by:

    1. Filip Stanek, 2021. "Optimal Out-of-Sample Forecast Evaluation under Stationarity," CERGE-EI Working Papers wp712, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    2. repec:bny:wpaper:0089 is not listed on IDEAS
    3. David Staines, 2023. "Stochastic Equilibrium the Lucas Critique and Keynesian Economics," Papers 2312.16214, arXiv.org, revised Jun 2024.
    4. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2023. "Machine learning advances for time series forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 76-111, February.
    5. Corradi, Valentina & Fosten, Jack & Gutknecht, Daniel, 2023. "Out-of-sample tests for conditional quantile coverage an application to Growth-at-Risk," Journal of Econometrics, Elsevier, vol. 236(2).
    6. Filip Staněk, 2023. "Optimal out‐of‐sample forecast evaluation under stationarity," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(8), pages 2249-2279, December.

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    More about this item

    Keywords

    inference; out-of-sample; prediction;
    All these keywords.

    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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