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Evaluating quantile-bounded and expectile-bounded interval forecasts

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  • Taylor, James W.

Abstract

In many different contexts, decision-making is improved by the availability of probabilistic predictions. The accuracy of probabilistic forecasting methods can be compared using scoring functions and insight provided by calibration tests. These tests evaluate the consistency of predictions with the observations. Our main agenda in this paper is interval forecasts and their evaluation. Such forecasts are usually bounded by two quantile forecasts. However, a limitation of quantiles is that they convey no information regarding the size of potential exceedances. By contrast, the location of an expectile is dictated by the whole distribution. This prompts us to propose expectile-bounded intervals. We provide interpretation, a consistent scoring function and a calibration test. Before doing this, we reflect on the evaluation of forecasts of quantile-bounded intervals and expectiles, and suggest extensions of previously proposed calibration tests in order to guard against strategic forecasting. We illustrate ideas using day-ahead electricity price forecasting.

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  • Taylor, James W., 2021. "Evaluating quantile-bounded and expectile-bounded interval forecasts," International Journal of Forecasting, Elsevier, vol. 37(2), pages 800-811.
    • Handle: RePEc:eee:intfor:v:37:y:2021:i:2:p:800-811
    DOI: 10.1016/j.ijforecast.2020.09.007
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    Cited by:

    1. Zhu, Bangzhu & Wan, Chunzhuo & Wang, Ping, 2022. "Interval forecasting of carbon price: A novel multiscale ensemble forecasting approach," Energy Economics, Elsevier, vol. 115(C).
    2. Janczura, Joanna & Wójcik, Edyta, 2022. "Dynamic short-term risk management strategies for the choice of electricity market based on probabilistic forecasts of profit and risk measures. The German and the Polish market case study," Energy Economics, Elsevier, vol. 110(C).
    3. James Mitchell & Martin Weale, 2023. "Censored density forecasts: Production and evaluation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(5), pages 714-734, August.
    4. Stephen Haben & Julien Caudron & Jake Verma, 2021. "Probabilistic Day-Ahead Wholesale Price Forecast: A Case Study in Great Britain," Forecasting, MDPI, vol. 3(3), pages 1-37, August.
    5. Norman Maswanganyi & Caston Sigauke & Edmore Ranganai, 2021. "Prediction of Extreme Conditional Quantiles of Electricity Demand: An Application Using South African Data," Energies, MDPI, vol. 14(20), pages 1-21, October.
    6. Candia, Claudio & Herrera, Rodrigo, 2024. "An empirical review of dynamic extreme value models for forecasting value at risk, expected shortfall and expectile," Journal of Empirical Finance, Elsevier, vol. 77(C).

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