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A Simple Method of Computing Prediction Intervals for Time Series Forecasts

Author

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  • Everette S. Gardner, Jr.

    (College of Business Administration, University of Houston, Houston, Texas 77004)

Abstract

Theoretical approaches to computing prediction intervals require strong assumptions that do not appear to hold in practice. This paper presents an empirical approach to prediction intervals that assumes very little. During model-fitting, variances of the errors are computed at different forecast leadtimes. Using these variances, the Chebyshev inequality is applied to determine prediction intervals. Empirical evidence is presented to show that this approach gives reasonable results. For example, using the 111 series in the M-competition, 95% prediction intervals actually contain 95.8% of post-sample observations.

Suggested Citation

  • Everette S. Gardner, Jr., 1988. "A Simple Method of Computing Prediction Intervals for Time Series Forecasts," Management Science, INFORMS, vol. 34(4), pages 541-546, April.
    • Handle: RePEc:inm:ormnsc:v:34:y:1988:i:4:p:541-546
    DOI: 10.1287/mnsc.34.4.541
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    Cited by:

    1. Taylor, James W., 2003. "Exponential smoothing with a damped multiplicative trend," International Journal of Forecasting, Elsevier, vol. 19(4), pages 715-725.
    2. Trapero, Juan R., 2016. "Calculation of solar irradiation prediction intervals combining volatility and kernel density estimates," Energy, Elsevier, vol. 114(C), pages 266-274.
    3. Allen, P. Geoffrey & Morzuch, Bernard J., 1995. "Comparing probability forecasts derived from theoretical distributions," International Journal of Forecasting, Elsevier, vol. 11(1), pages 147-157, March.
    4. Lee, Yun Shin & Scholtes, Stefan, 2014. "Empirical prediction intervals revisited," International Journal of Forecasting, Elsevier, vol. 30(2), pages 217-234.
    5. Mirakyan, Atom & Meyer-Renschhausen, Martin & Koch, Andreas, 2017. "Composite forecasting approach, application for next-day electricity price forecasting," Energy Economics, Elsevier, vol. 66(C), pages 228-237.
    6. Goodwin, Paul & Önkal, Dilek & Thomson, Mary, 2010. "Do forecasts expressed as prediction intervals improve production planning decisions?," European Journal of Operational Research, Elsevier, vol. 205(1), pages 195-201, August.
    7. Ling He & Chenyi Hu, 2009. "Impacts of Interval Computing on Stock Market Variability Forecasting," Computational Economics, Springer;Society for Computational Economics, vol. 33(3), pages 263-276, April.
    8. Gardner, Everette Jr., 2006. "Exponential smoothing: The state of the art--Part II," International Journal of Forecasting, Elsevier, vol. 22(4), pages 637-666.
    9. James W. Taylor & Derek W. Bunn, 1999. "A Quantile Regression Approach to Generating Prediction Intervals," Management Science, INFORMS, vol. 45(2), pages 225-237, February.
    10. Taylor, James W., 2007. "Forecasting daily supermarket sales using exponentially weighted quantile regression," European Journal of Operational Research, Elsevier, vol. 178(1), pages 154-167, April.
    11. Babai, M. Zied & Dai, Yong & Li, Qinyun & Syntetos, Aris & Wang, Xun, 2022. "Forecasting of lead-time demand variance: Implications for safety stock calculations," European Journal of Operational Research, Elsevier, vol. 296(3), pages 846-861.
    12. Taylor, James W. & Bunn, Derek W., 1999. "Investigating improvements in the accuracy of prediction intervals for combinations of forecasts: A simulation study," International Journal of Forecasting, Elsevier, vol. 15(3), pages 325-339, July.
    13. James W. Taylor, 2004. "Smooth transition exponential smoothing," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(6), pages 385-404.

    More about this item

    Keywords

    forecasting: time series;

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