Problem

Electricity price forecasting (EPF) is a critical yet challenging task for market participants due to the deregulated and highly volatile nature of electricity markets. Unlike other commodities, electricity cannot be easily stored, leading to complex price dynamics characterized by high volatility, non-constant mean and variance, and frequent price spikes. The increasing integration of renewable energy sources further complicates forecasting. Accurate EPF is essential for risk management, optimizing production and consumption, and making informed decisions to maximize profits and support climate goals. Existing statistical models often struggle with nonlinear dynamics, while purely deep learning models, despite their power, can be complex to tune and sometimes lack interpretability. There is a need for robust models that can capture both linear and nonlinear relationships, adapt to changing market conditions, and maintain interpretability.

Method

The paper proposes a novel parallel-branch recurrent neural network (RNN) architecture with skip connections for day-ahead electricity price forecasting. This hybrid model integrates three components: a linear expert model (LEM), an Elman RNN with ReLU activation for non-linear dynamics, and a Kalman filter (KF) which is an Elman RNN with identity activation for linear time dependencies. The model inputs include historical electricity prices (lagged), day-ahead load and renewable energy forecasts (wind, solar), fuel prices (Brent oil, natural gas, hard coal), carbon emission allowances (EUA), and calendar dummy variables. The data covers hourly observations from the largest European electricity market (Germany) between 2018 and 2025. A rolling forecasting scheme is employed for empirical testing, mimicking daily operations where the model is retrained on the most recent 1456 days, with parameters warm-started from the previous day's training. Hyperparameter optimization is performed using Optuna with a Tree-structured Parzen Estimator (TPE) sampler to find optimal configurations for learning rates, regularization parameters (L1 and L2), hidden layer size, sequence length, and training window sizes. The loss function minimizes Mean Squared Error (MSE) with L1 and L2 regularization.

Results

Empirical testing on hourly data from the German electricity market (2018-2025) demonstrated that the proposed hybrid architectures significantly improved forecasting accuracy. Among the stand-alone models, the Elman RNN (RMSE = 23.078) outperformed purely linear models (LEM: RMSE = 24.465, KF: RMSE = 25.352), highlighting the importance of capturing nonlinear dynamics. The best overall performance was achieved by the LEM-KF-RNN hybrid model, which yielded the lowest RMSE of 22.754, closely followed by the KF-RNN hybrid model (RMSE = 23.503). This represents approximately a 12% higher accuracy compared to leading benchmarks like Lasso Estimated AutoRegressive (LEAR) (RMSE = 26.587) and Deep Neural Network (DNN) (RMSE = 25.976) models. The Diebold-Mariano (DM) and Giacomini-White (GW) statistical tests confirmed the significant outperformance of the hybrid models over single models and benchmarks, with most differences between the best hybrid models being statistically insignificant. Forecast decomposition analysis showed that the LEM component effectively models baseline structural movements, while the RNN components (ReLU and identity) adaptively capture high-frequency deviations, such as price peaks, drops, and volatility spikes, leading to a more realistic and accurate combined forecast across varying market conditions.

Implications

The findings underscore the significant advantages of combining linear expert models, Kalman filters, and recurrent neural networks for day-ahead electricity price forecasting. The hybrid architecture effectively leverages the strengths of both linear and nonlinear modeling approaches, allowing it to capture a comprehensive range of stylized price characteristics, including calendar and autoregressive effects, as well as influences from load, renewable energy, and fuel/carbon markets. This enhanced accuracy, particularly in volatile market conditions like those experienced during the 2022 energy crisis, can lead to improved short-term decision-making and operational management in energy systems. Future research directions include exploring more advanced state-space models like Mamba for more adaptive temporal dependencies, dynamically determining the contribution of each branch in the hybrid model, and extending the proposed architecture to probabilistic forecasting to provide more comprehensive risk assessments for market participants. The model's interpretability, stemming from its linear components, also offers valuable insights into the influence of various market drivers.