# Combining predictive distributions of electricity prices: Does minimizing the CRPS lead to optimal decisions in day-ahead bidding?

arXiv: https://arxiv.org/abs/2308.15443 · HTML: https://mlsanity.com/paper/2308.15443/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 32 references that are in the map.
- First posted on arXiv 29 Aug 2023.

## Builds on (most cited first, 5 of 5)

- [Forecasting day-ahead electricity prices: A review of state-of-the-art algorithms, best practices and an open-access benchmark](https://mlsanity.com/paper/2008.08004/) (2020)
- [Forecast combinations: an over 50-year review](https://mlsanity.com/paper/2205.04216/) (2022)
- [Distributional neural networks for electricity price forecasting](https://mlsanity.com/paper/2207.02832/) (2022)
- [CRPS Learning](https://mlsanity.com/paper/2102.00968/) (2021)
- [Multivariate Probabilistic CRPS Learning with an Application to Day-Ahead Electricity Prices](https://mlsanity.com/paper/2303.10019/) (2023)

## Built on by (most cited first, 3 of 3)

- [Postprocessing of point predictions for probabilistic forecasting of day-ahead electricity prices: The benefits of using isotonic distributional regression](https://mlsanity.com/paper/2404.02270/) (2024)
- [Foundation models for electricity price forecasting and battery arbitrage: Can they replace market-specific forecasting models?](https://mlsanity.com/paper/2609.00089/) (2026)
- [Data-driven Calibration Sample Selection and Forecast Combination in Electricity Price Forecasting: An Application of the ARHNN Method](https://mlsanity.com/paper/2510.15011/) (2025)

## Abstract (arXiv)

Probabilistic price forecasting has recently gained attention in power trading because decisions based on such predictions can yield significantly higher profits than those made with point forecasts alone. At the same time, methods are being developed to combine predictive distributions, since no model is perfect and averaging generally improves forecasting performance. In this article we address the question of whether using CRPS learning, a novel weighting technique minimizing the continuous ranked probability score (CRPS), leads to optimal decisions in day-ahead bidding. To this end, we conduct an empirical study using hourly day-ahead electricity prices from the German EPEX market. We find that increasing the diversity of an ensemble can have a positive impact on accuracy. At the same time, the higher computational cost of using CRPS learning compared to an equal-weighted aggregation of distributions is not offset by higher profits, despite significantly more accurate predictions.