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A Quantile Regression Approach to Generating Prediction Intervals

Author

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  • James W. Taylor

    (London Business School, Sussex Place, Regents Park, London NW1 4SA, United Kingdom)

  • Derek W. Bunn

    (London Business School, Sussex Place, Regents Park, London NW1 4SA, United Kingdom)

Abstract

Exponential smoothing methods do not involve a formal procedure for identifying the underlying data generating process. The issue is then whether prediction intervals should be estimated by a theoretical approach, with the assumption that the method is optimal in some sense, or by an empirical procedure. In this paper we present an alternative hybrid approach which applies quantile regression to the empirical fit errors to produce forecast error quantile models. These models are functions of the lead time, as suggested by the theoretical variance expressions. In addition to avoiding the optimality assumption, the method is nonparametric, so there is no need for the common normality assumption. Application of the new approach to simple, Holt's, and damped Holt's exponential smoothing, using simulated and real data sets, gave encouraging results.

Suggested Citation

  • 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.
  • Handle: RePEc:inm:ormnsc:v:45:y:1999:i:2:p:225-237
    DOI: 10.1287/mnsc.45.2.225
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    References listed on IDEAS

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    1. Yar, Mohammed & Chatfield, Chris, 1990. "Prediction intervals for the Holt-Winters forecasting procedure," International Journal of Forecasting, Elsevier, vol. 6(1), pages 127-137.
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    Cited by:

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    2. Taylor, James W., 2003. "Exponential smoothing with a damped multiplicative trend," International Journal of Forecasting, Elsevier, vol. 19(4), pages 715-725.
    3. Cai, Zongwu & Xu, Xiaoping, 2009. "Nonparametric Quantile Estimations for Dynamic Smooth Coefficient Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 371-383.
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    15. Lee, Yun Shin & Scholtes, Stefan, 2014. "Empirical prediction intervals revisited," International Journal of Forecasting, Elsevier, vol. 30(2), pages 217-234.
    16. Derek Bunn, Arne Andresen, Dipeng Chen, Sjur Westgaard, 2016. "Analysis and Forecasting of Electricty Price Risks with Quantile Factor Models," The Energy Journal, International Association for Energy Economics, vol. 0(Number 1).
    17. Tom Pak Wing Fong & Alfred Yun Tong Wong, 2020. "Safehavenness of the Chinese renminbi," International Finance, Wiley Blackwell, vol. 23(2), pages 215-233, August.
    18. James W. Taylor, 2004. "Smooth transition exponential smoothing," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(6), pages 385-404.
    19. Gardner, Everette Jr., 2006. "Exponential smoothing: The state of the art--Part II," International Journal of Forecasting, Elsevier, vol. 22(4), pages 637-666.

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