Source-linked AI summary
Forecasting day-ahead electricity prices in Europe: the importance of considering market integration
Jesus Lago, Fjo De Ridder, Peter Vrancx, Bart De Schutter
TL;DR
The paper addresses limited general modeling of market integration in day-ahead electricity price forecasting, especially when neighboring prices are unavailable in advance. It proposes connected-market features, dual-market forecasting, and feature selection, finding statistically significant accuracy improvements and correct assessment of feature importance.
Problem
Existing market-integration forecasting methods assume neighboring day-ahead prices are known in advance, although most European markets release prices simultaneously, and they do not analyze market-integration relevance.
Method
The paper proposes a deep neural network using connected-market features, a feature-selection algorithm based on Bayesian optimization and functional analysis of variance, and a dual-market forecaster predicting prices in France and Belgium simultaneously.
Results
The proposed forecasters produce statistically significant improvements in predictive accuracy, while the feature-selection algorithm correctly assesses feature importance.
Takeaways & Limitations
Market integration can substantially modify electricity-price dynamics, and its features can improve forecasting accuracy in the Belgium–France case study.
Takeaways & Limitations
The case study concerns the Belgium and France electricity markets, while earlier market-integration methods were applicable only in limited situations because of their advance-price availability assumption.
Abstract
from arXiv · showhide
Motivated by the increasing integration among electricity markets, in this paper we propose two different methods to incorporate market integration in electricity price forecasting and to improve the predictive performance. First, we propose a deep neural network that considers features from connected markets to improve the predictive accuracy in a local market. To measure the importance of these features, we propose a novel feature selection algorithm that, by using Bayesian optimization and functional analysis of variance, evaluates the effect of the features on the algorithm performance. In addition, using market integration, we propose a second model that, by simultaneously predicting prices from two markets, improves the forecasting accuracy even further. As a case study, we consider the electricity market in Belgium and the improvements in forecasting accuracy when using various French electricity features. We show that the two proposed models lead to improvements that are statistically significant. Particularly, due to market integration, the predictive accuracy is improved from 15.7% to 12.5% sMAPE (symmetric mean absolute percentage error). In addition, we show that the proposed feature selection algorithm is able to perform a correct assessment, i.e. to discard the irrelevant features.
1. Introduction
Electricity prices are unusually dynamic because supply and demand must remain balanced while weather, calendar timing, and other external factors affect the market. Forecasting is therefore economically important and also relevant to grid stability, while market integration remains an underaddressed forecasting factor.
- Electricity prices exhibit sudden peaks and daily, weekly, and yearly seasonality because production, consumption, weather, and time influence market dynamics.
- Accurate price forecasting can mitigate economic effects of uncertainty and support market participants’ economic profits.
- Accurate forecasting also improves system stability by reducing risks associated with volatile prices, strategic-reserve use, and blackouts.
- The literature had not yet addressed how neighboring and connected markets influence forecasting accuracy despite increasing European market integration.
- The paper proposes two market-integration modeling approaches and reports statistically significant predictive improvements.
2. Literature Survey and Contributions
Prior forecasting research spans several methodological families, but evidence on model superiority is mixed and market-integration methods remain scarce and narrowly applicable. The paper addresses these gaps with general DNN-based integration models and a nonlinear feature-selection procedure.
- Electricity Price Forecasting: Electricity price forecasting research includes game-theoretic, fundamental, reduced-form, statistical, and artificial-intelligence methods.
- Electricity Price Forecasting: Statistical and artificial-intelligence methods have generally produced the best results for day-ahead electricity spot-price forecasting.
- Electricity Price Forecasting: Comparisons among forecasting models have yielded unclear conclusions, with effectiveness depending on the market and period studied.
- Market Integration: Evidence indicates increasing European market integration and strong common price dynamics between Belgium and France, but forecasting research on integration remains scarce.
- Market Integration: Existing integration approaches rely on neighboring-market day-ahead prices being known in advance, limiting their use where markets release prices simultaneously.
- Contributions: The paper proposes DNN forecasters using beforehand-available neighboring-market features and a multi-market output model that predicts prices simultaneously.
- Contributions: Its wrapper feature-selection algorithm uses functional ANOVA with nonlinear models and no feature transformation, while computing individual feature performance.
3. Preliminaries
The paper introduces standard deep neural networks, their training and generalization considerations, and Bayesian-optimization-based hyperparameter importance analysis using functional ANOVA.
- Deep neural networks: A standard DNN is a multilayer perceptron with more than one hidden layer, intended to improve generalization capabilities.The paper uses a standard DNN rather than convolutional or recurrent architectures.
- Deep neural networks: DNNs map inputs X to outputs Y through hidden-layer state vectors and weight-defined connections between neurons.The network parameters are the weights establishing the mapping connections.
- Training: Training estimates network weights by minimizing a problem-specific cost function over a finite training set.The cost can use measures such as the Euclidean norm or average cross-entropy.
- Training: Finite-set optimization can overfit, so training uses regularization techniques such as early stopping and out-of-sample evaluation.A model may perform well on training data but poorly on test data with a different distribution.
- Hyperparameter optimization: Bayesian optimization sequentially evaluates configurations, models the black-box performance function, and selects the best configuration after a fixed iteration budget.The paper uses Tree-Structured Parzen Estimation as its sequential model-based optimization algorithm.
- Hyperparameter importance: Functional ANOVA estimates hyperparameter importance by partitioning performance variance across hyperparameter subsets and evaluating their variance contributions.The method fits a random-forest performance predictor and derives marginal performance predictors for partial configurations.
3.4. Performance Metrics
The paper evaluates forecasting accuracy with sMAPE and tests whether differences between predictive models are statistically significant with the Diebold–Mariano test.
- sMAPE: sMAPE compares real and predicted outputs using symmetric absolute percentage errors across observations.The metric is selected because MAPE is sensitive to values close to zero.
- sMAPE: MAPE can be dominated by observations near zero because their percentage-error contributions become very large.This sensitivity motivates using sMAPE for electricity-price forecasting.
- Diebold–Mariano test: The Diebold–Mariano test assesses whether two forecasting models differ significantly in predictive accuracy.It tests equal expected loss using a loss differential constructed from forecast errors.
- Diebold–Mariano test: A one-sided Diebold–Mariano test compares a null of equal-or-worse accuracy for one model against the alternative that it is better.The loss function must produce a covariance-stationary loss differential.
4. Data
The study uses publicly available Belgian and French electricity-market data, including prices, grid forecasts, generation forecasts, and holidays, divided into training, validation, and test periods.
- Data sources: Inputs include day-ahead prices, grid-load forecasts, generation-capacity forecasts, and public-holiday calendars for Belgium and France.Prices come from EPEX-Belgium and EPEX-France, while forecasts come from the respective transmission system operators.
- Data selection: Weather data are omitted because weather effects are indirectly represented in transmission-system-operator forecasts and vary locally within countries.The paper therefore uses load and generation forecasts as more suitable cross-market variables for this study.
- Preprocessing: Price outliers are retained to preserve spikes, while missing and daylight-saving-related extra values are interpolated or removed.Neural-network training uses values normalized to [−1, 1], but metrics and tests use real prices.
- Data splits: The training, validation, and test sets cover model estimation, early stopping and selection, and out-of-sample evaluation, respectively.The validation and test sets each contain one year of data.
- Data sources: All data are publicly available through RTE, Elia, and the ENTSO-E transparency platform.This supports reproducibility of the experiments.
5. Modeling Framework
The modeling framework uses DNNs to forecast day-ahead prices from local and neighboring-market features, with single-market and dual-market output designs.
- Modeling framework: The paper proposes two market-integration models: one forecasts a single market using connected-market features, while the other jointly predicts prices in two markets.Both models forecast full sets of day-ahead prices but differ in output scope.
- Single-market forecaster: The single-market forecaster uses a two-hidden-layer DNN to predict 24 day-ahead prices from information available on the previous day.Inputs can include relevant data from local and neighboring markets.
- Single-market forecaster: The DNN uses weights and biases connecting the input, two hidden layers, and a 24-dimensional output price vector.Rectified linear units are used in hidden layers, with no output activation for real-valued prices.
- Training and selection: Feature selection and hyperparameter optimization determine the input dimension and the sizes of the two hidden layers.Training minimizes mean absolute error using Adam and early stopping.
- Dual-market forecaster: The dual-market forecaster predicts 48 prices jointly: 24 for market B and 24 for connected market F.Its implementation differs from the single-market model only in output size.
- Dual-market forecaster: Joint prediction is motivated by interrelated market dynamics and may improve generalization through shared features and regularization across related tasks.The paper identifies additional data and avoidance of single-task overfitting as possible explanations.
6. Feature Selection Algorithm
The proposed feature-selection method addresses two drawbacks of existing electricity-price feature-selection approaches by directly evaluating features within a nonlinear prediction model without transforming the original feature set.
- Existing methods select features without considering model performance and may transform inputs for nonlinear models, potentially losing feature information.
- The paper proposes a nonlinear wrapper method that evaluates features directly on the prediction model.
- The method is more computationally demanding but uses real predictive performance and avoids data transformations.
6.1. Algorithm Definition
The algorithm treats feature choices as hyperparameters, optimizes them with TPE, evaluates feature importance using functional ANOVA, and selects features based on importance and predicted marginal performance.
- Feature selection is organized into four steps: model features as hyperparameters, optimize them, analyze results, and select important features.
- Binary features represent inclusion or exclusion decisions, whereas integer features can also select an associated size or length.
- TPE optimization returns an optimal feature selection and feature-performance pairs linking each selection to model predictive accuracy.
- An optimal configuration alone may retain redundant features that do not affect performance, increasing computational cost and overfitting risk.
- Functional ANOVA estimates each feature’s and pairwise interaction’s percentage contribution to performance variance and predicts marginal performance for feature settings.
- Using a threshold, the final selection keeps features with sufficient individual or pairwise importance and removes those whose inclusion lowers predicted marginal performance.
- For integer features, selection considers both the feature and the instantiation with the best performance.
6.2. Case Study
The case study uses Bayesian optimization and functional ANOVA to select inputs for Belgian price forecasting, including French market features. After excluding unstable Belgian generation capacity, French prices and load explain about half of performance variance, guiding the final feature set.
- Feature Definition: The case study evaluates French electricity features as inputs for forecasting Belgian day-ahead prices.The available inputs include Belgian and French prices, load, generation, and public holidays.
- Feature Definition: The model represents loads, generation, and holidays as binary features, while Belgian price history uses integer selections for daily and weekly lags.French prices are included or excluded as a binary feature using the same lags as Belgian prices.
- Results: Removing gB reduced the sMAPE performance variance by a factor of 5 and produced a more distributed contribution across features.The revised experiment was designed to ensure more comparable conditions across training, validation, and test sets.
- Results: French prices and load accounted for roughly 50% of total performance variance, while French generation, Belgian load, and past-price history had minor roles.The selection also removed both public-holiday features and selected one weekly lag before marginal-performance analysis.
6.3. Discussion
The discussion identifies the selected French features as promising for Belgian price forecasting but emphasizes that their importance requires statistical confirmation. It also notes that the feature-selection algorithm itself still needs a direct accuracy evaluation.
- Discussion: The selected model inputs comprise French load and generation together with recent and weekly Belgian and French prices.These inputs summarize the feature-selection outcome discussed for the case study.
- Discussion: French market features appear important for forecasting accuracy, but the evidence supports only a general assessment of their importance.The authors state that statistical analysis is required before drawing further conclusions.
- Discussion: The feature-selection algorithm has not yet been evaluated directly against models retaining discarded features.Hypothesis testing of predictive-accuracy differences is proposed as a possible evaluation.
7. Evaluation of Market Integration and Modeling Framework
The evaluation tests whether French market information and dual-market forecasting improve Belgian day-ahead price predictions, using out-of-sample comparisons and Diebold–Mariano significance tests.
- Experimental setup: The evaluation compares Belgian-only models with models incorporating French data, and tests whether observed accuracy differences are statistically significant.The single-market setup contrasts MNoFR with MFR, while additional comparisons include Belgian load and dual-market forecasting.
- Single-market forecaster: French data significantly improves forecasting accuracy for all 24 Belgian day-ahead prices, according to individual-hour DM tests.The comparison remains statistically significant when Belgian load is included as a local regressor.
- Single-market forecaster: The full loss-differential DM test confirms the French-data improvement, with p-value 1.2·10^-11 without Belgian-load augmentation and 1.6·10^-12 with it.Both tests account for serial correlation.
- Feature-selection validation: Belgian load is not statistically relevant in the tested comparison, supporting the feature-selection algorithm’s decision to discard it.The authors note that this experiment evaluates the most problematic feature rather than all inputs.
- Dual-market forecaster: The dual-market forecaster improves significantly for 7 of 24 prices and is not significantly worse for the remaining 17.The full-sequence DM test also confirms a significant difference, with p-value 9.5·10^-03.
- Discussion: Overall, modeling market integration in the input space improves accuracy, while modeling it jointly in the output space yields further significant improvements.The case study also reports that French factors have greater influence on Belgian prices than several local Belgian features.
- Scope: The study excludes the Netherlands because less online data are available and Germany because there is no direct interconnection at the time of study.These choices constrain the markets considered in the case study.
8. Conclusions
The paper concludes that market integration can improve day-ahead electricity-price forecasting and that the proposed feature-selection method correctly assesses feature importance. The authors also discuss implications for policy, grid stability, and market-agent economics, while noting that further European markets remain to be studied.
- Contributions: The study proposes connected-market features and a dual-market forecaster to improve day-ahead price forecasting in Belgium and France.Both approaches produce statistically significant improvements in the case study.
- Conclusions: Market integration significantly enhances Belgian forecasting accuracy, and simultaneous prediction of French and Belgian prices can improve performance further.The authors attribute the dual-market benefit to learning more useful features and better generalizing price dynamics.
- Policy implications: The methodology could help policymakers evaluate market-integration regulations in other European regions.The conclusion links this possibility to observed changes in price dynamics between Belgium and France.
- Practical implications: Improved price-dynamics knowledge may benefit grid stability and market-agent economics by helping address price peaks and reducing costs.The paper gives savings of $1.5 million per year for a medium-size utility as an example of economic benefit from improved MAPE accuracy.
- Future work: The experiments should be expanded to other European markets to support broader policy analysis.This is identified as future work.
Copyright Information
The manuscript is distributed under the CC-BY-NC-ND 4.0 license.
- License: The manuscript version is made available under the CC-BY-NC-ND 4.0 license.The passage provides a link to the license.