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Multi-horizon uniform superior predictive ability revisited: A size-exploiting and consistent test

Author

Listed:
  • Verena Monschang
  • Mark Trede
  • Bernd Wilfling

Abstract

Quaedvlieg (2021, Journal of Business & Economic Statistics) proposes a uniform Superior Predictive Ability (uSPA) test for comparing forecasts across multiple horizons. The procedure is based on a 'minimum Diebold-Mariano' test statistic, and asymptotic critical values are obtained via bootstrapping. We show, theoretically and via simulations, that Quaedvlieg's test is subject to massive size distortions. In this article, we establish several convergence results for the 'minimum Diebold- Mariano' statistic, revealing that appropriate asymptotic critical values are given by the quantiles of the standard normal distribution. The uSPA test modified this way (i) always keeps the nominal size, (ii) is size-exploiting along the boundary that separates the parameter subsets of the null and the alternative uSPA hypotheses, and (iii) is consistent. Based on the closed skew normal distribution, we present a procedure for approximating the power function and demonstrate the favorable finite-sample properties of our test. In an empirical replication, we find that Quaedvlieg's (2021) results on uSPA comparisons between direct and iterative forecasting methods are statistically inconclusive.

Suggested Citation

  • Verena Monschang & Mark Trede & Bernd Wilfling, 2023. "Multi-horizon uniform superior predictive ability revisited: A size-exploiting and consistent test," CQE Working Papers 10623, Center for Quantitative Economics (CQE), University of Muenster.
    • Handle: RePEc:cqe:wpaper:10623
    as

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    File URL: https://www.wiwi.uni-muenster.de/cqe/sites/cqe/files/CQE_Paper/cqe_wp_106_2023.pdf
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    References listed on IDEAS

    as
    1. Marcellino, Massimiliano & Stock, James H. & Watson, Mark W., 2006. "A comparison of direct and iterated multistep AR methods for forecasting macroeconomic time series," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 499-526.
    2. Peter R. Hansen & Asger Lunde & James M. Nason, 2011. "The Model Confidence Set," Econometrica, Econometric Society, vol. 79(2), pages 453-497, March.
    3. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2008. "On the exact distribution of the maximum of absolutely continuous dependent random variables," Statistics & Probability Letters, Elsevier, vol. 78(1), pages 27-35, January.
    4. Jack Fosten & Daniel Gutknecht, 2021. "Horizon confidence sets," Empirical Economics, Springer, vol. 61(2), pages 667-692, August.
    5. de Jong, Robert M., 1997. "Central Limit Theorems for Dependent Heterogeneous Random Variables," Econometric Theory, Cambridge University Press, vol. 13(3), pages 353-367, June.
    6. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November.
    7. 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.
    8. Rogier Quaedvlieg, 2021. "Multi-Horizon Forecast Comparison," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(1), pages 40-53, January.
    9. repec:bla:econom:v:50:y:1983:i:197:p:3-17 is not listed on IDEAS
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Forecast evaluation; Joint-hypothesis testing; Stochastic dominance; Closed skew normal distribution;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: 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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