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Efficient estimation of forecast uncertainty based on recent forecast errors

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  • Knüppel, Malte

Abstract

Multi-step-ahead forecasts of the forecast uncertainty of an individual forecaster are often based on the horizon-specific sample means of his recent squared forecast errors, where the number of past forecast errors available decreases one-to-one with the forecast horizon. In this paper, the efficiency gains from the joint estimation of forecast uncertainty for all horizons in such samples are investigated. If the forecast uncertainty is estimated by seemingly unrelated regressions, it turns out that the covariance matrix of the squared forecast errors does not have to be estimated, but simply needs to have a certain structure, which is a very useful property in small samples. Considering optimal and non-optimal forecasts, it is found that the efficiency gains can be substantial for longer horizons in small samples. The superior performance of the seemingly-unrelated-regressions approach is confirmed in several empirical applications.

Suggested Citation

  • Knüppel, Malte, 2014. "Efficient estimation of forecast uncertainty based on recent forecast errors," International Journal of Forecasting, Elsevier, vol. 30(2), pages 257-267.
    • Handle: RePEc:eee:intfor:v:30:y:2014:i:2:p:257-267
    DOI: 10.1016/j.ijforecast.2013.08.004
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    1. Giordani, Paolo & Soderlind, Paul, 2003. "Inflation forecast uncertainty," European Economic Review, Elsevier, vol. 47(6), pages 1037-1059, December.
    2. Knüppel, Malte, 2014. "Efficient estimation of forecast uncertainty based on recent forecast errors," International Journal of Forecasting, Elsevier, vol. 30(2), pages 257-267.
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    9. Kajal Lahiri & Xuguang Sheng, 2010. "Measuring forecast uncertainty by disagreement: The missing link," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 514-538.
    10. Makridakis, Spyros & Hogarth, Robin M. & Gaba, Anil, 2009. "Forecasting and uncertainty in the economic and business world," International Journal of Forecasting, Elsevier, vol. 25(4), pages 794-812, October.
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    Cited by:

    1. Todd E. Clark & Michael W. McCracken & Elmar Mertens, 2020. "Modeling Time-Varying Uncertainty of Multiple-Horizon Forecast Errors," The Review of Economics and Statistics, MIT Press, vol. 102(1), pages 17-33, March.
    2. Lee, Seohyun, 2017. "Three essays on uncertainty: real and financial effects of uncertainty shocks," MPRA Paper 83617, University Library of Munich, Germany.
    3. Travis J. Berge, 2023. "Time-Varying Uncertainty of the Federal Reserve's Output Gap Estimate," The Review of Economics and Statistics, MIT Press, vol. 105(5), pages 1191-1206, September.
    4. Romanus, Eduardo E. & Silva, Eugênio & Goldschmidt, Ronaldo R., 2024. "Empirical probabilistic forecasting: An approach solely based on deterministic explanatory variables for the selection of past forecast errors," International Journal of Forecasting, Elsevier, vol. 40(1), pages 184-201.
    5. Knüppel, Malte, 2018. "Forecast-error-based estimation of forecast uncertainty when the horizon is increased," International Journal of Forecasting, Elsevier, vol. 34(1), pages 105-116.
    6. Clements, Michael P. & Galvão, Ana Beatriz, 2017. "Model and survey estimates of the term structure of US macroeconomic uncertainty," International Journal of Forecasting, Elsevier, vol. 33(3), pages 591-604.
    7. Knüppel, Malte, 2014. "Efficient estimation of forecast uncertainty based on recent forecast errors," International Journal of Forecasting, Elsevier, vol. 30(2), pages 257-267.
    8. David Reifschneider & Peter Tulip, 2017. "Gauging the Uncertainty of the Economic Outlook Using Historical Forecasting Errors: The Federal Reserve's Approach," RBA Research Discussion Papers rdp2017-01, Reserve Bank of Australia.

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    More about this item

    Keywords

    Multi-step-ahead forecasts; Forecast error variance; SUR; Forecasting practice;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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