Bayesian Neural Networks with Monte Carlo Dropout for Probabilistic Electricity Price Forecasting

Accurate electricity price forecasting is critical for strategic decision-making in deregulated electricity markets, where volatility stems from complex supply-demand dynamics and external factors. Traditional point forecasts often fail to capture inherent uncertainties, limiting their utility for risk management. This work presents a framework for probabilistic electricity price forecasting using Bayesian neural networks (BNNs) with Monte Carlo (MC) dropout, training separate models for each hour of the day to capture diurnal patterns. A critical assessment and comparison with the benchmark model, namely: generalized autoregressive conditional heteroskedasticity with exogenous variable (GARCHX) model and the LASSO estimated auto-regressive model (LEAR), highlights that the proposed model outperforms the benchmark models in terms of point prediction and intervals. This work serves as a reference for leveraging probabilistic neural models in energy market predictions.

💡 Research Summary

This research proposes a probabilistic framework for electricity price forecasting, specifically designed to address the high volatility and non-linear dynamics inherent in deregulated energy markets. While traditional forecasting methods focus on point predictions, this study leverages Bayesian Neural Networks (BNNs) combined with Monte Carlo (MC) Dropout to quantify predictive uncertainty, providing a more robust tool for risk management.

The methodological core of this paper lies in the implementation of an “Hourly Independent BNN” architecture. To mitigate the curse of dimensionality and the risk of overfitting that arises when attempting to model a full 24-hour cycle as a single high-dimensional vector, the authors trained separate models for each hour of the day. This approach allows the network to capture distinct diurnal and weekly patterns, such as price spikes and load fluctuations, more effectively. The input features consist of a 248-dimensional vector, including historical prices, residual load, renewable energy forecasts, and temporal dummies. By interpreting MC Dropout as a form of variational Bayesian inference, the model performs 1,000 forward passes during the inference stage to generate weight samples. The mean of these samples serves as the point prediction, while the variance quantifies both epistemic and aleatoric uncertainties.

The experimental evaluation utilized German Federal Network Agency data from 2017 to 2023. The proposed BNN was benchmarked against the GARCHX model (a traditional volatility model) and the LEAR model (a LASSO-based autoregressive model). The results demonstrate that while the BNN’s point prediction accuracy (MAE, RMSE, MAPE) is comparable to or slightly lower than the LEAR model, its performance in probabilistic metrics is superior. Specifically, the BNN provides a significantly narrower Mean Prediction Interval Width (MPIW), indicating more efficient and precise uncertainty intervals.

However, the study also reveals critical limitations. A significant discrepancy was observed in the Prediction Interval Coverage Probability (PICP), which reached only 0.11, far below the target 90% threshold. This suggests a lack of proper calibration, where the model’s predicted intervals fail to capture the true underlying distribution, potentially due to the approximations inherent in MC Dropout. Furthermore, the hourly independent structure fails to exploit the temporal continuity across the 24-hour period.

In conclusion, this work serves as a vital reference for utilizing probabilistic neural models in energy markets. Future research directions include integrating architectures like Transformers or Temporal Convolutions to preserve temporal dependencies and employing more sophisticated variational inference techniques, such as Flipout or Bayes by Backprop, to enhance the reliability and calibration of the predicted uncertainty intervals.