Recurrent Neural Networks with Linear Structures for Electricity Price Forecasting

TL;DR

This work introduces a parallel-branch neural network that fuses linear expert models, Kalman-filter-like state dynamics, and non-linear RNN components to forecast day-ahead electricity prices. Through extensive rolling-window experiments on German market data (2018–2025), the hybrid LEM-KF-RNN model achieves the lowest RMSE among evaluated architectures, outperforming traditional linear models and deep baselines. The study demonstrates that combining linear temporal structure with nonlinear sequence learning yields robust, interpretable forecasts, supported by comprehensive statistical testing and decomposition analysis. The approach offers a practical, adaptable framework for operational EPF with potential extensions to probabilistic forecasting and more advanced state-space methodologies.

Abstract

We present a novel recurrent neural network architecture designed explicitly for day-ahead electricity price forecasting, aimed at improving short-term decision-making and operational management in energy systems. Our combined forecasting model embeds linear structures, such as expert models and Kalman filters, into recurrent networks, enabling efficient computation and enhanced interpretability. The design leverages the strengths of both linear and non-linear model structures, allowing it to capture all relevant stylised price characteristics in power markets, including calendar and autoregressive effects, as well as influences from load, renewable energy, and related fuel and carbon markets. For empirical testing, we use hourly data from the largest European electricity market spanning 2018 to 2025 in a comprehensive forecasting study, comparing our model against state-of-the-art approaches, particularly high-dimensional linear and neural network models. The proposed model achieves approximately 12% higher accuracy than leading benchmarks. We evaluate the contributions of the interpretable model components and conclude on the impact of combining linear and non-linear structures.

Figures (13)

• Figure 1: Multi-panel time series for Germany's day-ahead electricity price and related feautures (2018–2025). The panels show: Electricity Price (EUR/MWh), Day-Ahead Load Forecasts, Wind Onshore Forecasts, Wind Offshore Forecasts, PV (Solar) Forecasts, and fuel prices comprising Coal, Natural Gas, Brent Oil, and EU ETS EUA Allowances, and time series split: Training sample (2018–2021), Validation sample (2021–2023), and Test sample (2023–2025).
• Figure 2: Rolling window and training strategy for electricity price forecasting. The approach consists of three phases: (1) Initial training on 4 years of historical data (from 10 October 2018 to 13 January 2021), (2) Rolling validation with weight transfer between windows (from 14 January 2021 to 14 January 2023), and (3) Rolling testing (from 15 January 2023 to 13 January 2025) with continuous model updates.
• Figure 3: Graph of a simple Elman network with one input, one hidden layer, and one output. The hidden state $\mathbf{h}_{t}$ is computed from the previous state $\mathbf{h}_{t-1}$ (dashed loop arrow) and the current input $\mathbf{x}_{t}$. The output $\mathbf{y}_{t} \in \mathbb{R}^{S}$ is then obtained through a linear transformation of the hidden state via the output weight matrix $\mathbf{W}_{\text{out}} \in \mathbb{R}^{S \times h}$ and bias term $\mathbf{b}_{\text{out}} \in \mathbb{R}^{S}$.
• Figure 4: A Parallel-Branch Recurrent Neural Network architecture with skip connections for day-ahead electricity price forecasting. The linear model for direct effects, an RNN branch for nonlinear temporal patterns, and the KF branch represents the Kalman Filter, which is for state-space dynamics. The outputs from the three branches are summed to produce 24-hour-ahead forecasts $(y_1, \ldots, y_{24})$.
• Figure 5: Features importance from the LEM component of the LEM-KF-RNN model across all hours.