1 Department of Electrical Engineering, Technical University of Denmark2 Center for Electric Power and Energy, Department of Electrical Engineering, Technical University of Denmark3 Department of Applied Mathematics and Computer Science, Technical University of Denmark4 Dynamical Systems, Department of Applied Mathematics and Computer Science, Technical University of Denmark
Research on generating and verification of multivariate probabilistic forecasts has gained increased interest over the last few years. Emphasis is placed here on the evaluation of forecast quality with the Energy score, which is based on a quadratic scoring rule. While this score may be seen as appealing since being proper, we show that its discrimination ability may be limited when focusing on the dependence structure of multivariate probabilistic forecasts. For the case of multivariate Gaussian process, a theoretical upper for such discrimination ability is derived and discussed. This limited discrimination ability may eventually get compromised by computational and sampling issues, as dimension increases.
Probabilistic forecasting; Energy score; Discrimination; Proper score; Multivariate scenarios