Analyzing Uncertainty Quantification in Statistical and Deep Learning Models for Probabilistic Electricity Price Forecasting
Andreas Lebedev, Abhinav Das, Sven Pappert, Stephan Schlüter
TL;DR
This study compares probabilistic electricity price forecasting methods that account for data and model uncertainty in the German day-ahead market using 2018–2024 data. It contrasts distributional deep nets augmented with ensembles, MC dropout, and conformal prediction against LEAR-based models with QRA, GARCH, and conformal prediction, alongside naive benchmarks. Across multiple metrics, LEAR variants emerge as strong, well-calibrated baselines, while DDNN, ensemble, and dropout methods improve probabilistic forecasts and stability; deep evidential regression underperforms in interval reliability. The results show ensemble- and CP-enhanced models can improve interval quality, but there is no universal winner across all point and probabilistic metrics, and trading performance depends on the chosen calibration and risk considerations. The work highlights the value of combining simple, interpretable statistical models with modern uncertainty-quantification techniques for risk-aware electricity price forecasting and decision-making.
Abstract
Precise probabilistic forecasts are fundamental for energy risk management, and there is a wide range of both statistical and machine learning models for this purpose. Inherent to these probabilistic models is some form of uncertainty quantification. However, most models do not capture the full extent of uncertainty, which arises not only from the data itself but also from model and distributional choices. In this study, we examine uncertainty quantification in state-of-the-art statistical and deep learning probabilistic forecasting models for electricity price forecasting in the German market. In particular, we consider deep distributional neural networks (DDNNs) and augment them with an ensemble approach, Monte Carlo (MC) dropout, and conformal prediction to account for model uncertainty. Additionally, we consider the LASSO-estimated autoregressive (LEAR) approach combined with quantile regression averaging (QRA), generalized autoregressive conditional heteroskedasticity (GARCH), and conformal prediction. Across a range of performance metrics, we find that the LEAR-based models perform well in terms of probabilistic forecasting, irrespective of the uncertainty quantification method. Furthermore, we find that DDNNs benefit from incorporating both data and model uncertainty, improving both point and probabilistic forecasting. Uncertainty itself appears to be best captured by the models using conformal prediction. Overall, our extensive study shows that all models under consideration perform competitively. However, their relative performance depends on the choice of metrics for point and probabilistic forecasting.