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Quantiles as optimal point forecasts

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  • Gneiting, Tilmann
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    Abstract

    Loss functions play a central role in the theory and practice of forecasting. If the loss function is quadratic, the mean of the predictive distribution is the unique optimal point predictor. If the loss is symmetric piecewise linear, any median is an optimal point forecast. Quantiles arise as optimal point forecasts under a general class of economically relevant loss functions, which nests the asymmetric piecewise linear loss, and which we refer to as generalized piecewise linear (GPL). The level of the quantile depends on a generic asymmetry parameter which reflects the possibly distinct costs of underprediction and overprediction. Conversely, a loss function for which quantiles are optimal point forecasts is necessarily GPL. We review characterizations of this type in the work of Thomson, Saerens and Komunjer, and relate to proper scoring rules, incentive-compatible compensation schemes and quantile regression. In the empirical part of the paper, the relevance of decision theoretic guidance in the transition from a predictive distribution to a point forecast is illustrated using the Bank of England's density forecasts of United Kingdom inflation rates, and probabilistic predictions of wind energy resources in the Pacific Northwest.

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    File URL: http://www.sciencedirect.com/science/article/B6V92-4YJFDT3-1/2/4adc6c085df2b16ef817d276a237dc99
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    Bibliographic Info

    Article provided by Elsevier in its journal International Journal of Forecasting.

    Volume (Year): 27 (2011)
    Issue (Month): 2 (April)
    Pages: 197-207

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    Handle: RePEc:eee:intfor:v:27:y::i:2:p:197-207

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    Web page: http://www.elsevier.com/locate/ijforecast

    Related research

    Keywords: Decision making Density forecasts Incentive-compatible compensation scheme Loss function Piecewise linear Proper scoring rule Quantile;

    References

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    Cited by:
    1. Xinxin Zhu & Marc Genton & Yingzhong Gu & Le Xie, 2014. "Space-time wind speed forecasting for improved power system dispatch," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 23(1), pages 1-25, March.
    2. Zhang, Yao & Wang, Jianxue & Wang, Xifan, 2014. "Review on probabilistic forecasting of wind power generation," Renewable and Sustainable Energy Reviews, Elsevier, vol. 32(C), pages 255-270.
    3. Georgios Anastasiades & Patrick McSharry, 2013. "Quantile Forecasting of Wind Power Using Variability Indices," Energies, MDPI, Open Access Journal, vol. 6(2), pages 662-695, February.
    4. Reason Lesego Machete, 2011. "Early Warning with Calibrated and Sharper Probabilistic Forecasts," Papers 1112.6390, arXiv.org, revised Jan 2012.

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