# Postprocessing of point predictions for probabilistic forecasting of day-ahead electricity prices: The benefits of using isotonic distributional regression

arXiv: https://arxiv.org/abs/2404.02270 · HTML: https://mlsanity.com/paper/2404.02270/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 45 references that are in the map.
- First posted on arXiv 2 Apr 2024.

## Builds on (most cited first, 14 of 14)

- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [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)
- [Neural networks for post-processing ensemble weather forecasts](https://mlsanity.com/paper/1805.09091/) (2018)
- [Neural basis expansion analysis with exogenous variables: Forecasting electricity prices with NBEATSx](https://mlsanity.com/paper/2104.05522/) (2021)
- [Isotonic Distributional Regression](https://mlsanity.com/paper/1909.03725/) (2019)
- [Generative machine learning methods for multivariate ensemble post-processing](https://mlsanity.com/paper/2211.01345/) (2022)
- [Distributional neural networks for electricity price forecasting](https://mlsanity.com/paper/2207.02832/) (2022)
- [Day-ahead electricity price forecasting with high-dimensional structures: Univariate vs. multivariate modeling frameworks](https://mlsanity.com/paper/1805.06649/) (2018)
- [CRPS Learning](https://mlsanity.com/paper/2102.00968/) (2021)
- [Conformal Prediction Interval Estimations with an Application to Day-Ahead and Intraday Power Markets](https://mlsanity.com/paper/1905.07886/) (2019)
- [Easy Uncertainty Quantification (EasyUQ): Generating Predictive Distributions from Single-valued Model Output](https://mlsanity.com/paper/2212.08376/) (2022)
- [Combining predictive distributions for statistical post-processing of ensemble forecasts](https://mlsanity.com/paper/1607.08096/) (2016)
- [A probabilistic forecast methodology for volatile electricity prices in the Australian National Electricity Market](https://mlsanity.com/paper/2311.07289/) (2023)
- [Combining predictive distributions of electricity prices: Does minimizing the CRPS lead to optimal decisions in day-ahead bidding?](https://mlsanity.com/paper/2308.15443/) (2023)

## Built on by (most cited first, 7 of 7)

- [Probabilistic measures afford fair comparisons of AIWP and NWP model output](https://mlsanity.com/paper/2506.03744/) (2025)
- [NBMLSS: probabilistic forecasting of electricity prices via Neural Basis Models for Location Scale and Shape](https://mlsanity.com/paper/2411.13921/) (2024)
- [Online Multivariate Regularized Distributional Regression for High-dimensional Probabilistic Electricity Price Forecasting](https://mlsanity.com/paper/2504.02518/) (2025)
- [Analyzing Uncertainty Quantification in Statistical and Deep Learning Models for Probabilistic Electricity Price Forecasting](https://mlsanity.com/paper/2509.19417/) (2025)
- [Foundation models for electricity price forecasting and battery arbitrage: Can they replace market-specific forecasting models?](https://mlsanity.com/paper/2609.00089/) (2026)
- [The Evolution of Probabilistic Price Forecasting Techniques: A Review of the Day-Ahead, Intra-Day, and Balancing Markets](https://mlsanity.com/paper/2511.05523/) (2025)
- [Stealing profits: Spread-based temporal hierarchy forecasting for day-ahead electricity markets](https://mlsanity.com/paper/2609.23223/) (2026)

## Abstract (arXiv)

Operational decisions relying on predictive distributions of electricity prices can result in significantly higher profits compared to those based solely on point forecasts. However, the majority of models developed in both academic and industrial settings provide only point predictions. To address this, we examine three postprocessing methods for converting point forecasts of day-ahead electricity prices into probabilistic ones: Quantile Regression Averaging, Conformal Prediction, and the recently introduced Isotonic Distributional Regression. We find that while the latter demonstrates the most varied behavior, it contributes the most to the ensemble of the three predictive distributions, as measured by Shapley values. Remarkably, the performance of the combination is superior to that of state-of-the-art Distributional Deep Neural Networks over two 4.5-year test periods from the German and Spanish power markets, spanning the COVID pandemic and the war in Ukraine.