Random Noise vs. State-of-the-Art Probabilistic Forecasting Methods: A Case Study on CRPS-Sum Discrimination Ability

Abstract

The recent developments in the machine-learning domain have enabled the development of complex multivariate probabilistic forecasting models. To evaluate the predictive power of these complex methods, it is pivotal to have a precise evaluation method to gauge the performance and predictability power of these complex methods. To do so, several evaluation metrics have been proposed in the past (such as the energy score, Dawid–Sebastiani score, and variogram score); however, these cannot reliably measure the performance of a probabilistic forecaster. Recently, CRPS-Sum has gained a lot of prominence as a reliable metric for multivariate probabilistic forecasting. This paper presents a systematic evaluation of CRPS-Sum to understand its discrimination ability. We show that the statistical properties of target data affect the discrimination ability of CRPS-Sum. Furthermore, we highlight that CRPS-Sum calculation overlooks the performance of the model on each dimension. These flaws can lead us to an incorrect assessment of model performance. Finally, with experiments on real-world datasets, we demonstrate that the shortcomings of CRPS-Sum provide a misleading indication of the probabilistic forecasting performance method. We illustrate that it is easily possible to have a better CRPS-Sum for a dummy model, which looks like random noise, in comparison to the state-of-the-art method.