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A validation frame for deterministic solar irradiance forecasts

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  • Morf, Heinrich

Abstract

A novel validation frame for deterministic solar irradiance forecasts is presented. It bases on the perception that a perfect forecast of a random variable must be indistinguishable from its observation. In mathematical terms: The random variables observation and forecast must be exchangeable. This implies that they have the same probability distribution and that the pertaining copula is symmetric. The validation frame tallies the equality of the probability distributions of observed and forecast solar irradiance, the symmetry of the pertaining copula, and the forecasting skill with well-defined measures, namely the Kolmogorov-Smirnov test statistic, copula asymmetry, and Spearman's ρ. The three measures are scale-invariant under strictly increasing transformations of observation and forecast. Thus, the frame is particularly suited for benchmarking solar irradiance forecasts from different locations, different calendar days, and over different periods. The frame is demonstrated on 24-h-ahead solar irradiance forecasts from two sites with different climates. Yet, it can be applied to any forecast of a continuous random variable. Additional theoretical insights connect the method to present-day practice, such as the Murphy-Winkler framework and the skill score.

Suggested Citation

  • Morf, Heinrich, 2021. "A validation frame for deterministic solar irradiance forecasts," Renewable Energy, Elsevier, vol. 180(C), pages 1210-1221.
    • Handle: RePEc:eee:renene:v:180:y:2021:i:c:p:1210-1221
    DOI: 10.1016/j.renene.2021.08.032
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    References listed on IDEAS

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    1. Liebscher, Eckhard, 2008. "Construction of asymmetric multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2234-2250, November.
    2. Roger Nelsen, 2007. "Extremes of nonexchangeability," Statistical Papers, Springer, vol. 48(4), pages 695-695, October.
    3. Morf, Heinrich, 2018. "Regression by Integration demonstrated on Ångström-Prescott-type relations," Renewable Energy, Elsevier, vol. 127(C), pages 713-723.
    4. Christian Genest & Johanna Nešlehová & Jean-François Quessy, 2012. "Tests of symmetry for bivariate copulas," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 811-834, August.
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