Isotonic Quantile Regression Averaging for uncertainty quantification of electricity price forecasts

TL;DR

This paper introduces Isotonic Quantile Regression Averaging (iQRA), a novel method for probabilistic electricity price forecasting that improves accuracy, reliability, and computational efficiency over existing methods.

Contribution

The paper proposes iQRA, which incorporates stochastic order constraints into quantile regression averaging, enhancing forecast calibration and reducing complexity without hyperparameters.

Findings

iQRA outperforms state-of-the-art methods in reliability and sharpness.

It produces well-calibrated prediction intervals across multiple confidence levels.

Isotonic regularization simplifies the model and aids variable selection.

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.