Isotonic Quantile Regression Averaging for uncertainty quantification of electricity price forecasts

2025-07-20

AI Summary

To address insufficient uncertainty quantification in electricity price forecasting—which hinders risk-informed decision-making—this paper proposes a novel probabilistic forecasting method based on ensemble point prediction. The method introduces (1) monotonicity and stochastic order constraints to enhance predictive calibration and reliability; (2) a hyperparameter-free variable selection mechanism that significantly reduces computational complexity; and (3) isotonic regression integrated within the quantile regression averaging (QRA) framework to refine ensemble-based uncertainty estimation. Empirical evaluation on the German day-ahead electricity market demonstrates that the proposed approach yields prediction intervals with superior reliability and sharpness across multiple confidence levels, consistently outperforming state-of-the-art post-processing methods.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Quantifying the uncertainty of forecasting models is essential to assess and mitigate the risks associated with data-driven decisions, especially in volatile domains such as electricity markets. Machine learning methods can provide highly accurate electricity price forecasts, critical for informing the decisions of market participants. However, these models often lack uncertainty estimates, which limits the ability of decision makers to avoid unnecessary risks. In this paper, we propose a novel method for generating probabilistic forecasts from ensembles of point forecasts, called Isotonic Quantile Regression Averaging (iQRA). Building on the established framework of Quantile Regression Averaging (QRA), we introduce stochastic order constraints to improve forecast accuracy, reliability, and computational costs. In an extensive forecasting study of the German day-ahead electricity market, we show that iQRA consistently outperforms state-of-the-art postprocessing methods in terms of both reliability and sharpness. It produces well-calibrated prediction intervals across multiple confidence levels, providing superior reliability to all benchmark methods, particularly coverage-based conformal prediction. In addition, isotonic regularization decreases the complexity of the quantile regression problem and offers a hyperparameter-free approach to variable selection.

Problem

• Quantify uncertainty in electricity price forecasts
• Improve forecast accuracy and reliability
• Reduce computational costs in quantile regression

Innovation

• Isotonic Quantile Regression Averaging for probabilistic forecasts
• Stochastic order constraints enhance accuracy and reliability
• Hyperparameter-free variable selection via isotonic regularization