PaperlayerView exact revision on arXiv

Source-linked AI summary

Deep Learning for Cross-Border Electricity Price Forecasting: A Comparative Study

Hadeer Elashhab, Sai Srijan Papineni, Marvin Dorn, Veit Hagenmeyer, Benjamin Schäfer

arXiv:2608.17091v1cs.LG

TL;DR

Electricity price forecasting lacks standardized benchmarks for comparing models across markets and data regimes. This study evaluates six deep learning architectures under cross-border low-data settings and finds that NBEATSx and N-HiTS perform reliably, while transformers require more tuning.

  • Problem

    Electricity price forecasting lacks reproducible benchmarks for comparing deep learning models across markets and data regimes.

  • Method

    The study compares six deep learning architectures across zero-shot, one-shot, and few-shot settings using public European market data and standardized procedures.

  • Results

    NBEATSx and N-HiTS perform reliably across scenarios, while transformers benefit from transfer learning but require more tuning and longer training histories.

  • Takeaways & Limitations

    Feature selection and temporal alignment can influence forecasting performance as much as model architecture in cross-border, low-data settings.

  • Takeaways & Limitations

    The study does not report results across multiple random seeds for every experiment, so outcomes may be affected by initialization bias.

Abstract

from arXiv · show

While publicly available electricity market data presents a valuable resource for forecasting research, the field lacks established benchmark datasets for standardized comparison. As a result, many studies have relied on different datasets and metrics to evaluate methods in isolated settings, making it difficult to assess progress and compare state-of-the-art approaches consistently. In this work, we use public data to evaluate deep learning models for electricity price forecasting (EPF) across multiple market settings. Our goal is to establish a reproducible framework that enables a consistent evaluation of forecasting models. Although deep learning has been explored for day-ahead EPF, many prior studies are limited to single-market settings, narrow feature sets, or fixed training regimes. This work presents a comparative evaluation of six deep learning models--covering state-space, MLP, RNN, and Transformer-based architectures--emphasizing generalization across markets. We simulate low-data target-market conditions using zero-shot, one-shot, and few-shot learning. Our test set focuses on the Germany-Luxembourg (DE-LU) bidding zone in 2024 using a standardized dataset with calendar, historical price, and market-derived features. Our findings suggest that N-HiTS and NBEATSx perform competitively in limited-data scenarios, while transformer-based models can reach comparable accuracy but tend to require more adaptation and tuning. Model performance also benefits from careful feature selection and hyperparameter tuning, and we note that the differences between the strongest models are often small.

I. INTRODUCTION · II. RELATED WORK

The introduction motivates electricity price forecasting as an actionable signal for renewable-energy integration and presents a reproducible, cross-market comparison of six deep learning models under limited target-market data. The related work shows progress in statistical, deep learning, spatial, exogenous-feature, transfer-learning, and probabilistic approaches, while identifying limited cross-market generalization and inconsistent evaluation as open gaps.

  • I. INTRODUCTION: Renewable energy integration is central to the transition toward sustainable energy systems and can reduce greenhouse-gas emissions and reliance on fossil fuels.The passage highlights wind, solar, and hydro as increasingly competitive with conventional energy sources.
  • I. INTRODUCTION: Electricity price forecasting supports energy-market decision-making by providing a compact signal of supply-demand imbalances, generation costs, grid constraints, and system stress or surplus.The passage presents EPF as complementary to weather forecasts for integrating weather-dependent renewable sources.
  • I. INTRODUCTION: The study compares six deep learning models across architectures, addressing literature dominated by isolated markets, short evaluation windows, and single-model assessments.The named architectures include N-HiTS, NBEATSx, TFT, Mamba, and additional models introduced in the continuation of the passage.
  • I. INTRODUCTION: The evaluation uses the full 2024 year and simulates cross-border target-market constraints through zero-shot, one-shot, and few-shot learning for DE-LU.Zero-shot uses no DE-LU training data, one-shot uses one sample, and few-shot uses a few samples.
  • I. INTRODUCTION: The study contributes a six-model comparison, a reproducible pipeline using public market data, and a benchmark for data-efficient and generalizable EPF.The authors aim to encourage broader use of the dataset through transparent evaluation and detailed experiments.
  • II. RELATED WORK: Earlier EPF research used ARIMA, GARCH, and VAR, while later comparisons found statistical methods effective for short horizons but less robust in highly dynamic or nonlinear environments.The related work also describes evaluations combining ARIMA(X), CNN-LSTM hybrids, and VAR models.
  • II. RELATED WORK: Recent EPF studies apply CNN-GRU, tuned LSTM, spatial coupling, NBEATSx, and MLP models, but often remain tied to specific markets, fixed regimes, or limited generalization settings.Prior work includes cross-border features, SHAP-based interpretability, exogenous inputs, and evaluations across 19 European bidding zones.
  • II. RELATED WORK: Transfer-learning studies pre-train on source markets and fine-tune on targets such as France and Germany, whereas probabilistic methods emphasize risk-aware decisions, uncertainty quantification, and explainability.These approaches generally do not benchmark zero-shot or few-shot learning, cross-market transferability, or generalization strategies within a unified framework.

III. DATA

The study uses Fraunhofer ISE’s publicly available day-ahead electricity price data for European bidding zones, with consistent coverage from 2015. Its dataset combines prices with calendar, market, load, cross-border, and generation-related variables, while restricting the analysis period to preserve consistent zone definitions after the DE-AT-LU split.

  • Data source: The data come from Fraunhofer ISE’s Energy Charts platform and API, providing day-ahead hourly spot prices for European bidding zones in EUR/MWh from 2015 onward.The platform’s license and terms of use are documented in Section A.
  • Market structure: Bidding zones are geographical areas with a single market-clearing electricity price, generally aligned with national borders but sometimes spanning or subdividing countries.Germany and Luxembourg share one bidding zone, whereas Italy has multiple zones.
  • Temporal scope: The dataset begins in the last quarter of 2018 to account for the split of the former DE-AT-LU zone into DE-LU and AT.This restriction maintains consistency in the spatial definition of price zones throughout the analysis.
  • Features: The primary dataset pairs day-ahead electricity prices with calendar features, market factors, electricity load, cross-border trading data, and energy generation shares.These exogenous variables are intended to represent key market dynamics influencing price formation.

NON-PRICE FEATURES … A. TRAINING AND TEST SETS

The framework combines cyclic calendar encodings, market-derived exogenous variables, and realistic pre-auction inputs to forecast DE-LU day-ahead prices. Models are trained on historical windows of varying lengths and evaluated consistently on 2024 prices across zero-shot, one-shot, and few-shot settings.

  • NON-PRICE FEATURES: Calendar inputs use sine/cosine and one-hot encodings for periodic variables, alongside binary indicators for temporal patterns.The encoded variables include day of week, month, and hour.
  • NON-PRICE FEATURES: Market features include natural gas, synthetic benchmark, CO2 allowance prices, and electricity load to represent supply-demand, regulatory, and economic drivers.The synthetic price combines gas prices and CO2 allowances to approximate DE-LU day-ahead price formation, using 55% plant efficiency and 0.4 tCO2/MWh emission intensity.
  • DATA KNOWN AT FORECASTING TIME: Forecasts use information available before the daily 12:00 CET EPEX SPOT auction for the following day’s 00:00–23:00 CET hourly intervals.The setup reflects the timing of uniform-price auctions in the DE-LU bidding zone.
  • DATA KNOWN AT FORECASTING TIME: The Full Previous Day strategy supplies the latest 24 hours, with weekly historical imputation for load and previous-day imputation for renewable and non-renewable generation.This approach targets realistic market conditions while maintaining consistent input quality.
  • IV. FRAMEWORK: The framework trains models on three historical spans: October 2018–December 2023, 2020–2023, and 2023.These datasets cover stable periods, the COVID-19 shock, the 2022 energy crisis, pandemic recovery, and recent market behavior.
  • A. TRAINING AND TEST SETS: The common test set contains DE-LU electricity prices for all of 2024 and is used across zero-shot, one-shot, and few-shot experiments.The 2024 test period includes price spikes and relatively stable periods under dynamic market conditions.
  • A. TRAINING AND TEST SETS: DE-LU is selected because it is Europe’s largest bidding zone, serves over 80 million people, and is highly interconnected with continental European and Nordic zones.The zone therefore provides a broad setting for evaluating forecasting generalization.
  • A. TRAINING AND TEST SETS: Training uses overlapping sliding windows with an hourly stride, although hyperparameter optimization may select a daily stride to reduce redundancy.Hourly strides increase samples and exposure to fine-grained temporal dependencies, whereas daily strides provide less exposure to short-term fluctuations.

B. MODEL SELECTION AND COMPARISON

The study compares six deep learning models spanning recurrent, MLP, state-space, and attention-based architectures for day-ahead electricity price forecasting. Standardized implementations and MAE/RMSE evaluation support comparison across temporal dependencies, exogenous-input handling, and computational complexity.

  • Model architectures: Six models—LSTM, NBEATSx, N-HiTS, Mamba, VT, and TFT—span recurrent, MLP, state-space, and attention-based architectures.The comparison covers temporal dependencies, exogenous-input handling, and longer-range forecasting.
  • Model architectures: LSTM uses gated memory cells to preserve information over extended time intervals and bridge long time lags.Input and output gates regulate information entering and leaving the cell.
  • Model architectures: NBEATSx extends N-BEATS with convolutional encoding of static and time-dependent exogenous variables, addressing covariate integration and interpretability.The original N-BEATS architecture was restricted to univariate data.
  • Model architectures: Mamba uses selective state-space modeling and recurrent scanning instead of attention or convolution, achieving linear scaling in sequence length.Its design omits standard attention and MLP layers and uses a fused kernel to reduce latent-state materialization.
  • Implementation and evaluation: All models except Mamba use Neu- ralForecast, while Mamba uses its official implementation extended for historical exogenous inputs; complexity ranges from linear to quadratic.Mamba has linear complexity, whereas transformer models have quadratic complexity.
  • Implementation and evaluation: Point forecasts are evaluated with mean absolute error (MAE) and root mean squared error (RMSE), while training uses absolute error for consistency with EPF literature.The evaluation follows common practices in electricity price forecasting.

C. INPUT FEATURES

All models use a shared feature set spanning calendar, future-known market, and historically reported variables. Zero-, one-, and few-shot experiments use only calendar features, whereas full-model training and tuning use all available exogenous features unless noted.

  • Input feature categories: All architectures are trained with a shared input-feature set organized into calendar, future-known market, and historically reported categories.This design promotes comparability across architectures.
  • Input feature categories: Calendar features include hour-of-day, day-of-week, month, weekends, and German public holidays.These features are always available.
  • Input feature categories: Future-known market variables include gas prices, CO2 emission allowances, and a derived synthetic price.
  • Input feature categories: Historically reported features include electricity load, renewable generation, and non-renewable generation, typically available up to 2 hours before the day-ahead auction.The auction is announced daily at 12:00 CET.
  • Feature-use regimes: Zero-, one-, and few-shot experiments use only calendar variables, while full-model training and tuning use all available exogenous features unless otherwise noted.This isolates generalization from exogenous market data in limited-data experiments.
  • Time representation and preprocessing: Feature extraction uses local CET time before conversion to UTC, preserving calendar relationships while avoiding daylight-saving-time duplication or gaps.The preprocessing supports temporal continuity and interpretability.

D. HYPERPARAMETER OPTIMIZATION · E. LEARNING STRATEGIES

The study systematically optimizes all six models with Bayesian hyperparameter search and evaluates DE-LU generalization under zero-shot, one-shot, and few-shot learning strategies. These strategies simulate practical forecasting with limited target-market data.

  • D. HYPERPARAMETER OPTIMIZATION: All six models are tuned with AutoModel and Optuna’s tree-structured parzen estimator for Bayesian optimization, using validation feedback to explore hyperparameters.The search spaces combine default recommendations with DAEPF-specific settings and the full input-feature set.
  • D. HYPERPARAMETER OPTIMIZATION: Model tuning uses a fixed 90/10 train-validation split or 6–12-fold cross-validation, depending on model type and dataset size.Lighter models receive up to 30 trials, while computationally intensive models are limited to 10 trials.
  • D. HYPERPARAMETER OPTIMIZATION: The Adam optimizer is used across all models because of its reliability in non-stationary environments.
  • E. LEARNING STRATEGIES: Three learning strategies assess generalization under different levels of DE-LU target-zone data availability.The strategies use DE-LU as the target zone.
  • E. LEARNING STRATEGIES: Zero-shot learning exposes models to no DE-LU data during training.
  • E. LEARNING STRATEGIES: One-shot learning uses a single DE-LU training sample with a 7-day input window and a 1-day, or 24h, forecast horizon.
  • E. LEARNING STRATEGIES: Few-shot learning uses 30 consecutive days of DE-LU data.
  • E. LEARNING STRATEGIES: These learning settings simulate practical forecasting scenarios in which target-market data may be limited.Table 1 summarizes DE-LU exposure under each strategy.

V. RESULTS · A. MODELS · 1) Baseline Models

The study evaluates simple historical-price and market-factor baselines before introducing deep learning models. Previous Day’s Price is the strongest baseline and becomes the primary benchmark, while other methods struggle with volatility or achieve higher errors.

  • 1) Baseline Models: The baseline evaluation provides intuitive reference points for measuring the added value of more complex forecasting models.
  • 1) Baseline Models: Synthetic Price estimates electricity prices from gas prices and CO2 emission certificates using a formula defined in Equation (1).
  • 1) Baseline Models: Previous Day’s Price assigns each hour the price observed at the same hour on the preceding day.
  • 1) Baseline Models: Previous Week’s Price uses the same hour from seven days earlier, whereas Previous Month’s Price uses the corresponding hour from the previous month.
  • 1) Baseline Models: 27.85 MAE and 44.35 RMSE: Previous Day’s Price achieves the lowest errors among all baselines.
  • 1) Baseline Models: Previous Week and Previous Month produce the highest MAE and RMSE values, while Synthetic Price ranks second but has noticeably higher error.
  • 1) Baseline Models: Previous Day’s Price closely tracks actual prices during stable periods but misses sudden spikes; Synthetic Price remains relatively flat and misses short-term volatility.
  • 1) Baseline Models: Because it performs best, Previous Day’s Price is adopted as the primary reference benchmark for subsequent deep learning evaluations.

2) Deep learning models · B. EXOGENOUS FEATURE ABLATION

Deep-learning models generally outperform baseline methods, with TFT strongest when calendar features are included and NBEATSx strongest using electricity prices alone. Exogenous features can help selectively, but adding more inputs does not consistently improve accuracy and may degrade performance.

  • 2) Deep learning models: TFT achieves the lowest MAE and RMSE with calendar features, while NBEATSx achieves the lowest MAE and RMSE using electricity prices alone.Both models benefit from calendar information, indicating that weekdays and holidays may provide useful predictive signals.
  • 2) Deep learning models: Deep-learning models consistently outperform the baseline methods evaluated in the study.The comparison uses the same test period and 7-day input window, although model-specific training start years were tuned.
  • 2) Deep learning models: LSTM degrades with calendar features, while VT shows the weakest overall performance, potentially reflecting overfitting, limited inductive bias, or insufficient regularization.These findings concern the model comparisons reported with minimally tuned default implementations and selected training configurations.
  • 2) Deep learning models: Mamba’s MAE falls from 27.45 to 22.72 when calendar features are included, suggesting benefits from structured temporal inputs.The improvement occurs despite Mamba’s relatively simple design.
  • B. EXOGENOUS FEATURE ABLATION: NBEATSx achieves the best MAE (20.90) with gas only, whereas N-HiTS performs best with gas, CO2, and synthetic prices but without load, reaching MAE 20.20 and RMSE 35.11.For many models, gas and synthetic price features provide modest gains, while adding more features can produce diminishing returns.
  • B. EXOGENOUS FEATURE ABLATION: LSTM performs best with gas and calendar inputs, but additional features increase error, indicating sensitivity to noisy inputs.Its best performance is obtained using only electricity prices and calendar features.
  • B. EXOGENOUS FEATURE ABLATION: VT performs poorly across all exogenous-feature configurations, while overall results show that additional inputs do not guarantee better performance.The ablation uses a fixed 7-day input window and always includes calendar features and electricity prices.
  • B. EXOGENOUS FEATURE ABLATION: Mamba achieves MAE = 22.51 using only gas prices, outperforming its calendar-only counterpart, while further exogenous features degrade accuracy.This suggests Mamba may be better suited to clean, low-dimensional inputs.

C. HYPERPARAMETER OPTIMIZATION · D. CROSS-ZONE GENERALIZATION: ZERO-SHOT,

Model-specific hyperparameter tuning identifies compact feature sets and suitable historical windows, while cross-zone experiments show broadly comparable low-data performance across architectures. NBEATSx benefits modestly from target-market examples, whereas TFT and VT perform best zero-shot, with VT improving substantially after tuning and transfer learning.

  • C. HYPERPARAMETER OPTIMIZATION: Model-specific tuning evaluates electricity-price, calendar, and relevant exogenous features, with best configurations reported in Table 5.Mamba and LSTM are excluded from this tuning round because of time constraints and weaker or insufficiently tuned performance.
  • C. HYPERPARAMETER OPTIMIZATION: NBEATSx, N-HiTS, and TFT perform best with gas, CO2, and synthetic-price features while omitting load, supporting moderate feature sets.The feature-selection pattern aligns with the ablation findings that more extensive inputs may not improve performance.
  • C. HYPERPARAMETER OPTIMIZATION: N-HiTS achieves the lowest MAE (18.75) and RMSE (34.77), attributed to hierarchical interpolation and decomposition.The optimal training windows begin in 2020 for NBEATSx and N-HiTS, and in 2018 for TFT.
  • D. CROSS-ZONE GENERALIZATION: ZERO-SHOT,: Cross-zone experiments transfer models trained on the multi-zone dataset excluding DE-LU to 2024 DE-LU forecasts while varying included target-zone data.For training-range selection, data from 2015 onward outperforms starts in October 2018 or January 2020.
  • D. CROSS-ZONE GENERALIZATION: ZERO-SHOT,: Across models and learning strategies, MAE remains roughly 18.5–19.4, so differences are small and may partly reflect run-to-run variability.The study does not report results across multiple seeds, making the trends tentative.
  • D. CROSS-ZONE GENERALIZATION: ZERO-SHOT,: NBEATSx reaches its lowest MAE in one-shot learning (18.48), followed by few-shot (18.57) and zero-shot (18.96).The authors suggest a single target-market example may help calibration, although the effect is small.
  • D. CROSS-ZONE GENERALIZATION: ZERO-SHOT,: Overall, the four architectures perform comparably under low-data cross-zone conditions, with modest sensitivity to the amount of target-market data.The paper notes that repeated runs and statistical significance testing are needed to confirm these trends.

VI. LIMITATIONS AND FUTURE WORK

The study’s comparative EPF framework has limitations in tuning scope, statistical reporting, computational documentation, and modeling novelty. Future work should strengthen benchmarking, reproducibility, probabilistic and foundation-model evaluation, and interpretability for decision support.

  • Hyperparameter optimization and feature selection: Hyperparameter searches use constrained spaces and limited trials, motivating broader optimization, especially for high-capacity models sensitive to initialization such as TFT and VT.The tuning is performed with Optuna but is restricted by time and resource constraints.
  • Statistical robustness and reporting: MAE and RMSE do not fully capture operational forecasting behavior, so future evaluations should add rMAE, sMAPE, cost-sensitive, and directional metrics.The analysis also primarily reports best-performing configurations rather than broader experimental variation.
  • Computational documentation: Computational records omit systematic GPU-memory, batch-size, per-trial training-time, and CO2-footprint logging, limiting reproducibility and meaningful training comparisons.Training times and hardware are recorded only for final model runs.
  • Scope of modeling contributions: The study evaluates existing deep learning EPF models rather than introducing a novel architecture, establishing a reproducible baseline before targeted architectural innovation.The authors frame systematic comparison and documentation as prerequisites for developing new models.
  • Next steps: Future extensions include probabilistic forecasting, EPF transferability tests for foundation models, and interpretability tools such as SHAP, attention attribution, and counterfactual explanations.These directions are intended to improve transparency and decision support, particularly in high-stakes applications.

VII. CONCLUSION

The study compares six deep learning architectures and three learning strategies for day-ahead electricity price forecasting across markets, using consistent 2024 DE-LU test data. It finds that NBEATSx and N-HiTS are reliable in multiple scenarios, while feature design, temporal alignment, and model-dependent adaptation shape low-data performance.

  • Study scope: The evaluation covers six architectures and zero-shot, one-shot, and few-shot learning using consistent 2024 test data from the DE-LU bidding zone.The study focuses on cross-border generalization in day-ahead electricity price forecasting.
  • Main findings: NBEATSx and N-HiTS perform reliably across multiple scenarios, especially with calendar features and selected exogenous variables.Differences between the strongest models are often small and should be confirmed across repeated runs.
  • Feature and data effects: Input feature design and temporal alignment can be as influential as model architecture, with selective exogenous variables often outperforming broad or complex inputs.Small amounts of target-market data can improve low-data performance, although the benefit depends on the model.
  • Research contribution: The study supports reproducible EPF benchmarks by examining generalization across markets and data regimes under realistic operational constraints.It uses a publicly available dataset and standardized training procedures based on existing implementations.

APPENDIX B COMPUTATIONAL RESOURCES

Computational efficiency is presented as an important complement to predictive accuracy for real-world deployment. Training times are reported separately from hyperparameter optimization, which adds substantial computational cost.

  • Operational model selection must balance predictive accuracy against computational efficiency, because marginal accuracy gains may not justify substantially higher resource requirements.This consideration is especially relevant for real-world deployment.
  • Table 7 reports approximate full-dataset training-time ranges for the tested models on a GPU-enabled system.The reported values exclude hyperparameter optimization.
  • 3 to 4 hours were required for hyperparameter optimization across the tested models, depending on iteration count and model complexity.Experiments ran on BwUniCluster nodes equipped with NVIDIA A100 and H100 GPUs.
Loading 2608.17091v1…