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Assessing point forecast accuracy by stochastic error distance

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  • Francis X. Diebold
  • Minchul Shin

Abstract

We propose point forecast accuracy measures based directly on distance of the forecast-error c.d.f. from the unit step function at 0 (“stochastic error distance,” or SED). We provide a precise characterization of the relationship between SED and standard predictive loss functions, and we show that all such loss functions can be written as weighted SEDs. The leading case is absolute error loss. Among other things, this suggests shifting attention away from conditional-mean forecasts and toward conditional-median forecasts.

Suggested Citation

  • Francis X. Diebold & Minchul Shin, 2017. "Assessing point forecast accuracy by stochastic error distance," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 588-598, October.
    • Handle: RePEc:taf:emetrv:v:36:y:2017:i:6-9:p:588-598
    DOI: 10.1080/07474938.2017.1307247
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    1. Graham Elliott & Allan Timmermann & Ivana Komunjer, 2005. "Estimation and Testing of Forecast Rationality under Flexible Loss," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(4), pages 1107-1125.
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    5. Valentina Corradi & Norman Swanson, 2013. "A Survey of Recent Advances in Forecast Accuracy Comparison Testing, with an Extension to Stochastic Dominance," Departmental Working Papers 201309, Rutgers University, Department of Economics.
    6. Gneiting, Tilmann, 2011. "Quantiles as optimal point forecasts," International Journal of Forecasting, Elsevier, vol. 27(2), pages 197-207, April.
    7. Patton, Andrew J. & Timmermann, Allan, 2007. "Testing Forecast Optimality Under Unknown Loss," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1172-1184, December.
    8. Lee, Tae-Hwy & Tu, Yundong & Ullah, Aman, 2014. "Nonparametric and semiparametric regressions subject to monotonicity constraints: Estimation and forecasting," Journal of Econometrics, Elsevier, vol. 182(1), pages 196-210.
    9. Xiaohong Chen & Norman R. Swanson (ed.), 2013. "Recent Advances and Future Directions in Causality, Prediction, and Specification Analysis," Springer Books, Springer, edition 127, number 978-1-4614-1653-1, November.
    10. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    11. Jin, Sainan & Corradi, Valentina & Swanson, Norman R., 2017. "Robust Forecast Comparison," Econometric Theory, Cambridge University Press, vol. 33(6), pages 1306-1351, December.
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    Cited by:

    1. Borgonovo, Emanuele & Hazen, Gordon B. & Jose, Victor Richmond R. & Plischke, Elmar, 2021. "Probabilistic sensitivity measures as information value," European Journal of Operational Research, Elsevier, vol. 289(2), pages 595-610.
    2. Francis X. Diebold & Minchul Shin & Boyuan Zhang, 2020. "On the Aggregation of Probability Assessments: Regularized Mixtures of Predictive Densities for Eurozone Inflation and Real Interest Rates," Papers 2012.11649, arXiv.org, revised Jun 2022.
    3. Diebold, Francis X. & Shin, Minchul, 2015. "Assessing point forecast accuracy by stochastic loss distance," Economics Letters, Elsevier, vol. 130(C), pages 37-38.
    4. Emilian Dobrescu, 2014. "Attempting to Quantify the Accuracy of Complex Macroeconomic Forecasts," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(4), pages 5-21, December.
    5. Tomás Marinozzi, 2023. "Forecasting Inflation in Argentina: A Probabilistic Approach," Ensayos Económicos, Central Bank of Argentina, Economic Research Department, vol. 1(81), pages 81-110, May.
    6. Jin, Sainan & Corradi, Valentina & Swanson, Norman R., 2017. "Robust Forecast Comparison," Econometric Theory, Cambridge University Press, vol. 33(6), pages 1306-1351, December.
    7. Valentina Corradi & Sainan Jin & Norman R. Swanson, 2023. "Robust forecast superiority testing with an application to assessing pools of expert forecasters," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(4), pages 596-622, June.
    8. Hiroyuki Kawakatsu, 2020. "Recovering Yield Curves from Dynamic Term Structure Models with Time-Varying Factors," Stats, MDPI, vol. 3(3), pages 1-46, August.

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    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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