Implementations of some scoring functions discussed in the paper.
extremal_score(x, y, theta, functional = "expectile", alpha = 0.5)apl_score(x, y, alpha = 0.5)
ase_score(x, y, alpha = 0.5)
Numeric vector of forecasts
Numeric vector of realizations (same length as x)
Threshold parameter for extremal score (must be a numeric scalar)
String, either "expectile" or "quantile"
Level of the quantile or expectile, must be a numeric scalar in the (0,1) interval
All functions return a vector of scores (same length as x and y). Smaller scores correspond to better forecasts.
extremal_score is the scoring function defined in Equations (10) and (12) of Ehm et al (2016). apl_score is the asymmetric piecewise scoring function for quantiles, see Equation (6) in Ehm et al (2016). ase_score is the asymmetric squared error for expectiles, see Equation (8) in Ehm et al (2016).
Ehm, W., Gneiting, T., Jordan, A. and Krueger, F. (2016): Of Quantiles and Expectiles: Consistent Scoring Functions, Choquet Representations, and Forecast Rankings. Journal of the Royal Statistical Society (Series B) 78, 1-29. 10.1111/rssb.12154 (open access).