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.

With the rapid development of electricity markets, price volatility has significantly increased, making accurate forecasting crucial for power system operations and market decisions. Traditional linear models cannot capture the complex nonlinear characteristics of electricity pricing, necessitating advanced machine learning approaches. This study compares eight machine learning models using Spanish electricity market data, integrating consumption, generation, and meteorological variables. The models evaluated include linear regression, ridge regression, decision tree, KNN, random forest, gradient boosting, SVR, and XGBoost. Results show that KNN achieves the best performance with R^2 of 0.865, MAE of 3.556, and RMSE of 5.240. To enhance interpretability, LIME analysis reveals that meteorological factors and supply-demand indicators significantly influence price fluctuations through nonlinear relationships. This work demonstrates the effectiveness of machine learning models in electricity price forecasting while improving decision transparency through interpretability analysis.

Electricity price forecasting has become a critical tool for decision-making in energy markets, particularly as the increasing penetration of renewable energy introduces greater volatility and uncertainty. Historically, research in this field has been dominated by point forecasting methods, which provide single-value predictions but fail to quantify uncertainty. However, as power markets evolve due to renewable integration, smart grids, and regulatory changes, the need for probabilistic forecasting has become more pronounced, offering a more comprehensive approach to risk assessment and market participation. This paper presents a review of probabilistic forecasting methods, tracing their evolution from Bayesian and distribution based approaches, through quantile regression techniques, to recent developments in conformal prediction. Particular emphasis is placed on advancements in probabilistic forecasting, including validity-focused methods which address key limitations in uncertainty estimation. Additionally, this review extends beyond the Day-Ahead Market to include the Intra-Day and Balancing Markets, where forecasting challenges are intensified by higher temporal granularity and real-time operational constraints. We examine state of the art methodologies, key evaluation metrics, and ongoing challenges, such as forecast validity, model selection, and the absence of standardised benchmarks, providing researchers and practitioners with a comprehensive and timely resource for navigating the complexities of modern electricity markets.

Accurate prediction of electricity prices is crucial for stakeholders in the energy market, particularly for grid operators, energy producers, and consumers. This study focuses on developing a predictive model leveraging Long Short-Term Memory (LSTM) networks to forecast day-ahead electricity prices in the California energy market. The model incorporates a variety of features, including historical price data, weather conditions, and the energy generation mix. A novel custom loss function that integrates Mean Absolute Error (MAE), Jensen-Shannon Divergence (JSD), and a smoothness penalty is introduced to enhance the prediction accuracy and interpretability. Additionally, an online learning approach is implemented to allow the model to adapt to new data incrementally, ensuring continuous relevance and accuracy. The results demonstrate that the custom loss function can improve the model's performance, aligning predicted prices more closely with actual values, particularly during peak intervals. Also, the online learning model outperforms other models by effectively incorporating real-time data, resulting in lower prediction error and variability. The inclusion of the energy generation mix further enhances the model's predictive capabilities, highlighting the importance of comprehensive feature integration. This research provides a robust framework for electricity price forecasting, offering valuable insights and tools for better decision-making in dynamic electricity markets.

Calibration sample selection and forecast combination are two simple yet powerful tools used in forecasting. They can be combined with a variety of models to significantly improve prediction accuracy, at the same time offering easy implementation and low computational complexity. While their effectiveness has been repeatedly confirmed in prior scientific literature, the topic is still underexplored in the field of electricity price forecasting. In this research article we apply the Autoregressive Hybrid Nearest Neighbors (ARHNN) method to three long-term time series describing the German, Spanish and New England electricity markets. We show that it outperforms popular literature benchmarks in terms of forecast accuracy by up to 10%. We also propose two simplified variants of the method, granting a vast decrease in computation time with only minor loss of prediction accuracy. Finally, we compare the forecasts' performance in a battery storage system trading case study. We find that using a forecast-driven strategy can achieve up to 80% of theoretical maximum profits while trading, demonstrating business value in practical applications.

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.

Abstract--While neural networks are achieving high predictive accuracy in multi-horizon probabilistic forecasting, understanding the underlying mechanisms that lead to feature-conditioned outputs remains a significant challenge for forecasters. In this work, we take a further step toward addressing this critical issue by introducing the Quantile Neural Basis Model, which incorporates the interpretability principles of Quantile Generalized Additive Models into an end-to-end neural network training framework. T o this end, we leverage shared basis decomposition and weight factorization, complementing Neural Models for Location, Scale, and Shape by avoiding any parametric distributional assumptions. We validate our approach on day-ahead electricity price forecasting, achieving predictive performance comparable to distributional and quantile regression neural networks, while offering valuable insights into model behavior through the learned nonlinear mappings from input features to output predictions across the horizon. The challenge of probabilistic electricity price forecasting (PEPF) in day-ahead power markets constitutes a critical research area with significant practical implications.

This study evaluates deep neural networks for forecasting probability distributions of financial returns. 1D convolutional neural networks (CNN) and Long Short-Term Memory (LSTM) architectures are used to forecast parameters of three probability distributions: Normal, Student's t, and skewed Student's t. Using custom negative log-likelihood loss functions, distribution parameters are optimized directly. The models are tested on six major equity indices (S\&P 500, BOVESPA, DAX, WIG, Nikkei 225, and KOSPI) using probabilistic evaluation metrics including Log Predictive Score (LPS), Continuous Ranked Probability Score (CRPS), and Probability Integral Transform (PIT). Results show that deep learning models provide accurate distributional forecasts and perform competitively with classical GARCH models for Value-at-Risk estimation. The LSTM with skewed Student's t distribution performs best across multiple evaluation criteria, capturing both heavy tails and asymmetry in financial returns. This work shows that deep neural networks are viable alternatives to traditional econometric models for financial risk assessment and portfolio management.

--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 A veraging (iQRA). Building on the established framework of Quantile Regression A veraging (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. The primary goal of a point forecasting model is to provide an accurate prediction of the future value of a variable of interest to aid in the decision making process [1].

Electricity markets are highly complex, involving lots of interactions and complex dependencies that make it hard to understand the inner workings of the market and what is driving prices. Econometric methods have been developed for this, white-box models, however, they are not as powerful as deep neural network models (DNN). In this paper, we use a DNN to forecast the price and then use XAI methods to understand the factors driving the price dynamics in the market. The objective is to increase our understanding of how different electricity markets work. To do that, we apply explainable methods such as SHAP and Gradient, combined with visual techniques like heatmaps (saliency maps) to analyse the behaviour and contributions of various features across five electricity markets. We introduce the novel concepts of SSHAP values and SSHAP lines to enhance the complex representation of high-dimensional tabular models.