mlsanityData to 14 Oct 2026

Online Multivariate Regularized Distributional Regression for High-dimensional Probabilistic Electricity Price Forecasting

arXiv 2504.02518 ↗First posted 3 Apr 2025stat.ML econ.EM q-fin.STcited by 2

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Abstract (arXiv)

Probabilistic electricity price forecasting (PEPF) is vital for short-term electricity markets, yet the multivariate nature of day-ahead prices - spanning 24 consecutive hours - remains underexplored. At the same time, real-time decision-making requires methods that are both accurate and fast. We introduce an online algorithm for multivariate distributional regression models, allowing efficient modeling of the conditional means, variances, and dependence structures of electricity prices. The approach combines multivariate distributional regression with online coordinate descent and LASSO-type regularization (absolute shrinkage and selection operator), enabling scalable estimation in high-dimensional covariate spaces. Additionally, we propose a regularized estimation path over increasingly complex dependence structures, allowing for early stopping and avoiding overfitting. In a case study using historical data from the German day-ahead market, the proposed method yields interpretable and well-calibrated joint prediction intervals for the 24-dimensional price distribution and provides robust performance across a range of proper scoring rules. The results underscore the importance of modeling the dependence structure of electricity prices. Furthermore, we analyze the trade-off between predictive accuracy and computational costs for batch and online estimation and provide a high-performing open-source Python implementation in the ondil package.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 31 of its 92 references that are in the map. First posted on arXiv 3 Apr 2025.

Builds on

31 of 92 references.

References · 31

  1. 2021Adaptive Conformal Inference Under Distribution Shiftcited by 375
  2. 2022Adaptive Conformal Predictions for Time Seriescited by 161
  3. 2021Activation Functions in Deep Learning: A Comprehensive Survey and Benchmarkcited by 155
  4. 2019High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processescited by 148
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  6. 2020Forecasting day-ahead electricity prices: A review of state-of-the-art algorithms, best practices and an open-access benchmarkcited by 108
  7. 2020Semi-Structured Distributional Regression -- Extending Structured Additive Models by Arbitrary Deep Neural Networks and Data Modalitiescited by 24
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  10. 2019Conformal Prediction Interval Estimations with an Application to Day-Ahead and Intraday Power Marketscited by 19
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19 more
  1. 2021M5 Competition Uncertainty: Overdispersion, distributional forecasting, GAMLSS and beyondcited by 11
  2. 2021Evaluating the Discrimination Ability of Proper Multivariate Scoring Rulescited by 8
  3. 2019Multivariate Forecasting Evaluation: On Sensitive and Strictly Proper Scoring Rulescited by 7
  4. 2021Cholesky-based multivariate Gaussian regressioncited by 7
  5. 2023Regions of Reliability in the Evaluation of Multivariate Probabilistic Forecastscited by 7
  6. 2024Postprocessing of point predictions for probabilistic forecasting of day-ahead electricity prices: The benefits of using isotonic distributional regressioncited by 7
  7. 2019Marginally-calibrated deep distributional regressioncited by 6
  8. 2021Using the Softplus Function to Construct Alternative Link Functions in Generalized Linear Models and Beyondcited by 5
  9. 2024On-line conformalized neural networks ensembles for probabilistic forecasting of day-ahead electricity pricescited by 5
  10. 2020Probabilistic multivariate electricity price forecasting using implicit generative ensemble post-processingcited by 4
  11. 2020Online Missing Value Imputation and Change Point Detection with the Gaussian Copulacited by 4
  12. 2022Bidding and Scheduling in Energy Markets: Which Probabilistic Forecast Do We Need?cited by 4
  13. 2022Multi-Target XGBoostLSS Regressioncited by 4
  14. 2023Multivariate Probabilistic CRPS Learning with an Application to Day-Ahead Electricity Pricescited by 4
  15. 2024Online Distributional Regressioncited by 3
  16. 2021Variable Selection Using a Smooth Information Criterion for Distributional Regression Modelscited by 2
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  18. 2024NBMLSS: probabilistic forecasting of electricity prices via Neural Basis Models for Location Scale and Shapecited by 2
  19. 2022Additive Covariance Matrix Models: Modelling Regional Electricity Net-Demand in Great Britaincited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 1.

2 papers.

  1. 2025Probabilistic intraday electricity price forecasting using generative machine learningcited by 2
  2. 2026Electricity Price Forecasting: Bridging Linear Models, Neural Networks and Online Learningcited by 1