IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2504.02518.html
   My bibliography  Save this paper

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

Author

Listed:
  • Simon Hirsch

Abstract

Probabilistic electricity price forecasting (PEPF) is a key task for market participants in short-term electricity markets. The increasing availability of high-frequency data and the need for real-time decision-making in energy markets require online estimation methods for efficient model updating. We present an online, multivariate, regularized distributional regression model, allowing for the modeling of all distribution parameters conditional on explanatory variables. Our approach is based on the combination of the multivariate distributional regression and an efficient online learning algorithm based on online coordinate descent for LASSO-type regularization. Additionally, we propose to regularize the estimation along a path of increasingly complex dependence structures of the multivariate distribution, allowing for parsimonious estimation and early stopping. We validate our approach through one of the first forecasting studies focusing on multivariate probabilistic forecasting in the German day-ahead electricity market while using only online estimation methods. We compare our approach to online LASSO-ARX-models with adaptive marginal distribution and to online univariate distributional models combined with an adaptive Copula. We show that the multivariate distributional regression, which allows modeling all distribution parameters - including the mean and the dependence structure - conditional on explanatory variables such as renewable in-feed or past prices provide superior forecasting performance compared to modeling of the marginals only and keeping a static/unconditional dependence structure. Additionally, online estimation yields a speed-up by a factor of 80 to over 400 times compared to batch fitting.

Suggested Citation

  • Simon Hirsch, 2025. "Online Multivariate Regularized Distributional Regression for High-dimensional Probabilistic Electricity Price Forecasting," Papers 2504.02518, arXiv.org.
    • Handle: RePEc:arx:papers:2504.02518
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2504.02518
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Katarzyna Maciejowska & Weronika Nitka, 2024. "Multiple split approach -- multidimensional probabilistic forecasting of electricity markets," Papers 2407.07795, arXiv.org.
    2. Francis X. Diebold, 2015. "Comparing Predictive Accuracy, Twenty Years Later: A Personal Perspective on the Use and Abuse of Diebold-Mariano Tests," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 1-1, January.
    3. Groll, Andreas & Hambuckers, Julien & Kneib, Thomas & Umlauf, Nikolaus, 2019. "LASSO-type penalization in the framework of generalized additive models for location, scale and shape," Computational Statistics & Data Analysis, Elsevier, vol. 140(C), pages 59-73.
    4. Berrisch, Jonathan & Ziel, Florian, 2024. "Multivariate probabilistic CRPS learning with an application to day-ahead electricity prices," International Journal of Forecasting, Elsevier, vol. 40(4), pages 1568-1586.
    5. Lipiecki, Arkadiusz & Uniejewski, Bartosz & Weron, Rafał, 2024. "Postprocessing of point predictions for probabilistic forecasting of day-ahead electricity prices: The benefits of using isotonic distributional regression," Energy Economics, Elsevier, vol. 139(C).
    6. C. Alexander & M. Coulon & Y. Han & X. Meng, 2024. "Evaluating the discrimination ability of proper multi-variate scoring rules," Annals of Operations Research, Springer, vol. 334(1), pages 857-883, March.
    7. Marcjasz, Grzegorz & Narajewski, Michał & Weron, Rafał & Ziel, Florian, 2023. "Distributional neural networks for electricity price forecasting," Energy Economics, Elsevier, vol. 125(C).
    8. Kath, Christopher & Ziel, Florian, 2021. "Conformal prediction interval estimation and applications to day-ahead and intraday power markets," International Journal of Forecasting, Elsevier, vol. 37(2), pages 777-799.
    9. Nadja Klein & Michael Stanley Smith & David J. Nott, 2023. "Deep distributional time series models and the probabilistic forecasting of intraday electricity prices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(4), pages 493-511, June.
    10. Tilmann Gneiting & Fadoua Balabdaoui & Adrian E. Raftery, 2007. "Probabilistic forecasts, calibration and sharpness," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 243-268, April.
    11. Ziel, Florian & Weron, Rafał, 2018. "Day-ahead electricity price forecasting with high-dimensional structures: Univariate vs. multivariate modeling frameworks," Energy Economics, Elsevier, vol. 70(C), pages 396-420.
    12. Jonathan Berrisch & Florian Ziel, 2023. "Multivariate Probabilistic CRPS Learning with an Application to Day-Ahead Electricity Prices," Papers 2303.10019, arXiv.org, revised Feb 2024.
    13. Mashlakov, Aleksei & Kuronen, Toni & Lensu, Lasse & Kaarna, Arto & Honkapuro, Samuli, 2021. "Assessing the performance of deep learning models for multivariate probabilistic energy forecasting," Applied Energy, Elsevier, vol. 285(C).
    14. Casella, Francesco & Bachmann, Bernhard, 2021. "On the choice of initial guesses for the Newton-Raphson algorithm," Applied Mathematics and Computation, Elsevier, vol. 398(C).
    15. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    16. Agakishiev, Ilyas & Härdle, Wolfgang Karl & Kopa, Milos & Kozmik, Karel & Petukhina, Alla, 2025. "Multivariate probabilistic forecasting of electricity prices with trading applications," Energy Economics, Elsevier, vol. 141(C).
    17. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    18. Lago, Jesus & Marcjasz, Grzegorz & De Schutter, Bart & Weron, Rafał, 2021. "Forecasting day-ahead electricity prices: A review of state-of-the-art algorithms, best practices and an open-access benchmark," Applied Energy, Elsevier, vol. 293(C).
    19. Paul F. V. Wiemann & Thomas Kneib & Julien Hambuckers, 2024. "Using the softplus function to construct alternative link functions in generalized linear models and beyond," Statistical Papers, Springer, vol. 65(5), pages 3155-3180, July.
    20. Muniain, Peru & Ziel, Florian, 2020. "Probabilistic forecasting in day-ahead electricity markets: Simulating peak and off-peak prices," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1193-1210.
    21. Billé, Anna Gloria & Gianfreda, Angelica & Del Grosso, Filippo & Ravazzolo, Francesco, 2023. "Forecasting electricity prices with expert, linear, and nonlinear models," International Journal of Forecasting, Elsevier, vol. 39(2), pages 570-586.
    22. Messner, Jakob W. & Pinson, Pierre, 2019. "Online adaptive lasso estimation in vector autoregressive models for high dimensional wind power forecasting," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1485-1498.
    23. Serinaldi, Francesco, 2011. "Distributional modeling and short-term forecasting of electricity prices by Generalized Additive Models for Location, Scale and Shape," Energy Economics, Elsevier, vol. 33(6), pages 1216-1226.
    24. Grothe, Oliver & Kächele, Fabian & Krüger, Fabian, 2023. "From point forecasts to multivariate probabilistic forecasts: The Schaake shuffle for day-ahead electricity price forecasting," Energy Economics, Elsevier, vol. 120(C).
    25. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
    26. David Rügamer & Chris Kolb & Nadja Klein, 2024. "Semi-Structured Distributional Regression," The American Statistician, Taylor & Francis Journals, vol. 78(1), pages 88-99, January.
    27. Kolkmann, Sven & Ostmeier, Lars & Weber, Christoph, 2024. "Modeling multivariate intraday forecast update processes for wind power," Energy Economics, Elsevier, vol. 139(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Simon Hirsch & Jonathan Berrisch & Florian Ziel, 2024. "Online Distributional Regression," Papers 2407.08750, arXiv.org, revised Aug 2024.
    2. Chȩć, Katarzyna & Uniejewski, Bartosz & Weron, Rafał, 2025. "Extrapolating the long-term seasonal component of electricity prices for forecasting in the day-ahead market," Journal of Commodity Markets, Elsevier, vol. 37(C).
    3. Katarzyna Chk{e}'c & Bartosz Uniejewski & Rafa{l} Weron, 2025. "Extrapolating the long-term seasonal component of electricity prices for forecasting in the day-ahead market," Papers 2503.02518, arXiv.org.
    4. Hauzenberger, Niko & Pfarrhofer, Michael & Rossini, Luca, 2025. "Sparse time-varying parameter VECMs with an application to modeling electricity prices," International Journal of Forecasting, Elsevier, vol. 41(1), pages 361-376.
    5. Grothe, Oliver & Kächele, Fabian & Krüger, Fabian, 2023. "From point forecasts to multivariate probabilistic forecasts: The Schaake shuffle for day-ahead electricity price forecasting," Energy Economics, Elsevier, vol. 120(C).
    6. Yang, Yifan & Guo, Ju’e & Li, Yi & Zhou, Jiandong, 2024. "Forecasting day-ahead electricity prices with spatial dependence," International Journal of Forecasting, Elsevier, vol. 40(3), pages 1255-1270.
    7. Katarzyna Maciejowska & Bartosz Uniejewski & Rafa{l} Weron, 2022. "Forecasting Electricity Prices," Papers 2204.11735, arXiv.org.
    8. Jozef Barunik & Lubos Hanus, 2023. "Learning Probability Distributions of Day-Ahead Electricity Prices," Papers 2310.02867, arXiv.org, revised Oct 2023.
    9. Micha{l} Narajewski & Florian Ziel, 2020. "Ensemble Forecasting for Intraday Electricity Prices: Simulating Trajectories," Papers 2005.01365, arXiv.org, revised Aug 2020.
    10. Hilger, Hannes & Witthaut, Dirk & Dahmen, Manuel & Rydin Gorjão, Leonardo & Trebbien, Julius & Cramer, Eike, 2024. "Multivariate scenario generation of day-ahead electricity prices using normalizing flows," Applied Energy, Elsevier, vol. 367(C).
    11. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    12. Narajewski, Michał & Ziel, Florian, 2020. "Ensemble forecasting for intraday electricity prices: Simulating trajectories," Applied Energy, Elsevier, vol. 279(C).
    13. Oliver Grothe & Fabian Kachele & Fabian Kruger, 2022. "From point forecasts to multivariate probabilistic forecasts: The Schaake shuffle for day-ahead electricity price forecasting," Papers 2204.10154, arXiv.org.
    14. Simon Hirsch & Florian Ziel, 2023. "Multivariate Simulation-based Forecasting for Intraday Power Markets: Modelling Cross-Product Price Effects," Papers 2306.13419, arXiv.org.
    15. Michał Narajewski, 2022. "Probabilistic Forecasting of German Electricity Imbalance Prices," Energies, MDPI, vol. 15(14), pages 1-17, July.
    16. Lipiecki, Arkadiusz & Uniejewski, Bartosz & Weron, Rafał, 2024. "Postprocessing of point predictions for probabilistic forecasting of day-ahead electricity prices: The benefits of using isotonic distributional regression," Energy Economics, Elsevier, vol. 139(C).
    17. Nowotarski, Jakub & Weron, Rafał, 2018. "Recent advances in electricity price forecasting: A review of probabilistic forecasting," Renewable and Sustainable Energy Reviews, Elsevier, vol. 81(P1), pages 1548-1568.
    18. Weronika Nitka & Rafał Weron, 2023. "Combining predictive distributions of electricity prices. Does minimizing the CRPS lead to optimal decisions in day-ahead bidding?," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 33(3), pages 105-118.
    19. Nickelsen, Daniel & Müller, Gernot, 2025. "Bayesian hierarchical probabilistic forecasting of intraday electricity prices," Applied Energy, Elsevier, vol. 380(C).
    20. Rafal Weron & Florian Ziel, 2018. "Electricity price forecasting," HSC Research Reports HSC/18/08, Hugo Steinhaus Center, Wroclaw University of Science and Technology.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2504.02518. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.