IDEAS home Printed from https://ideas.repec.org/a/eee/appene/v380y2025ics0306261924023596.html
   My bibliography  Save this article

Bayesian hierarchical probabilistic forecasting of intraday electricity prices

Author

Listed:
  • Nickelsen, Daniel
  • Müller, Gernot

Abstract

We address the need for forecasting methodologies that handle large uncertainties in electricity prices for continuous intraday markets by incorporating parameter uncertainty and using a broad set of covariables. This study presents the first Bayesian forecasting of electricity prices traded on the German intraday market. Endogenous and exogenous covariables are handled via Orthogonal Matching Pursuit (OMP) and regularising priors. The target variable is the IDFull price index, with forecasts given as posterior predictive distributions. Validation uses the highly volatile 2022 electricity prices, which have seldom been studied. As a benchmark, we use all intraday transactions at the time of forecast to compute a live IDFull value. According to market efficiency, it should not be possible to improve on this last-price benchmark. However, we observe significant improvements in point measures and probability scores, including an average reduction of 5.9% in absolute errors and an average increase of 1.7% in accuracy when forecasting whether the IDFull exceeds the day-ahead price. Finally, we challenge the use of LASSO in electricity price forecasting, showing that OMP results in superior performance, specifically an average reduction of 22.7% in absolute error and 20.2% in the continuous ranked probability score.

Suggested Citation

  • Nickelsen, Daniel & Müller, Gernot, 2025. "Bayesian hierarchical probabilistic forecasting of intraday electricity prices," Applied Energy, Elsevier, vol. 380(C).
  • Handle: RePEc:eee:appene:v:380:y:2025:i:c:s0306261924023596
    DOI: 10.1016/j.apenergy.2024.124975
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0306261924023596
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.apenergy.2024.124975?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Brusaferri, Alessandro & Matteucci, Matteo & Portolani, Pietro & Vitali, Andrea, 2019. "Bayesian deep learning based method for probabilistic forecast of day-ahead electricity prices," Applied Energy, Elsevier, vol. 250(C), pages 1158-1175.
    2. Uniejewski, Bartosz & Marcjasz, Grzegorz & Weron, Rafał, 2019. "Understanding intraday electricity markets: Variable selection and very short-term price forecasting using LASSO," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1533-1547.
    3. Simon Hirsch & Florian Ziel, 2024. "Simulation-based Forecasting for Intraday Power Markets: Modelling Fundamental Drivers for Location, Shape and Scale of the Price Distribution," The Energy Journal, , vol. 45(3), pages 87-124, May.
    4. Panagiotelis, Anastasios & Smith, Michael, 2008. "Bayesian density forecasting of intraday electricity prices using multivariate skew t distributions," International Journal of Forecasting, Elsevier, vol. 24(4), pages 710-727.
    5. Narajewski, Michał & Ziel, Florian, 2020. "Econometric modelling and forecasting of intraday electricity prices," Journal of Commodity Markets, Elsevier, vol. 19(C).
    6. Tim Janke & Florian Steinke, 2019. "Forecasting the Price Distribution of Continuous Intraday Electricity Trading," Energies, MDPI, vol. 12(22), pages 1-14, November.
    7. Grzegorz Marcjasz & Bartosz Uniejewski & Rafał Weron, 2020. "Beating the Naïve—Combining LASSO with Naïve Intraday Electricity Price Forecasts," Energies, MDPI, vol. 13(7), pages 1-16, April.
    8. Jozef Barunik & Lubos Hanus, 2023. "Learning Probability Distributions of Day-Ahead Electricity Prices," Papers 2310.02867, arXiv.org, revised Oct 2023.
    9. 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.
    10. Brenda López Cabrera & Franziska Schulz, 2017. "Forecasting Generalized Quantiles of Electricity Demand: A Functional Data Approach," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 127-136, January.
    11. Maciejowska, Katarzyna & Nitka, Weronika & Weron, Tomasz, 2021. "Enhancing load, wind and solar generation for day-ahead forecasting of electricity prices," Energy Economics, Elsevier, vol. 99(C).
    12. Katarzyna Maciejowska & Bartosz Uniejewski & Tomasz Serafin, 2020. "PCA Forecast Averaging—Predicting Day-Ahead and Intraday Electricity Prices," Energies, MDPI, vol. 13(14), pages 1-19, July.
    13. Le, Hong Lam & Ilea, Valentin & Bovo, Cristian, 2019. "Integrated European intra-day electricity market: Rules, modeling and analysis," Applied Energy, Elsevier, vol. 238(C), pages 258-273.
    14. Micha{l} Narajewski, 2022. "Probabilistic forecasting of German electricity imbalance prices," Papers 2205.11439, arXiv.org.
    15. Kath, Christopher & Ziel, Florian, 2018. "The value of forecasts: Quantifying the economic gains of accurate quarter-hourly electricity price forecasts," Energy Economics, Elsevier, vol. 76(C), pages 411-423.
    16. Michał Narajewski & Florian Ziel, 2019. "Estimation and Simulation of the Transaction Arrival Process in Intraday Electricity Markets," Energies, MDPI, vol. 12(23), pages 1-16, November.
    17. Michał Narajewski, 2022. "Probabilistic Forecasting of German Electricity Imbalance Prices," Energies, MDPI, vol. 15(14), pages 1-17, July.
    18. Cramer, Eike & Witthaut, Dirk & Mitsos, Alexander & Dahmen, Manuel, 2023. "Multivariate probabilistic forecasting of intraday electricity prices using normalizing flows," Applied Energy, Elsevier, vol. 346(C).
    19. José R. Andrade & Jorge Filipe & Marisa Reis & Ricardo J. Bessa, 2017. "Probabilistic Price Forecasting for Day-Ahead and Intraday Markets: Beyond the Statistical Model," Sustainability, MDPI, vol. 9(11), pages 1-29, October.
    20. Christopher Kath & Florian Ziel, 2020. "Optimal Order Execution in Intraday Markets: Minimizing Costs in Trade Trajectories," Papers 2009.07892, arXiv.org, revised Oct 2020.
    21. Hu, Xiao & Jaraitė, Jūratė & Kažukauskas, Andrius, 2021. "The effects of wind power on electricity markets: A case study of the Swedish intraday market," Energy Economics, Elsevier, vol. 96(C).
    22. Marcjasz, Grzegorz & Narajewski, Michał & Weron, Rafał & Ziel, Florian, 2023. "Distributional neural networks for electricity price forecasting," Energy Economics, Elsevier, vol. 125(C).
    23. Tomasz Serafin & Bartosz Uniejewski & Rafał Weron, 2019. "Averaging Predictive Distributions Across Calibration Windows for Day-Ahead Electricity Price Forecasting," Energies, MDPI, vol. 12(13), pages 1-12, July.
    24. Marcel Kremer & Rüdiger Kiesel & Florentina Paraschiv, 2020. "Intraday Electricity Pricing of Night Contracts," Energies, MDPI, vol. 13(17), pages 1-14, September.
    25. Ilkay Oksuz & Umut Ugurlu, 2019. "Neural Network Based Model Comparison for Intraday Electricity Price Forecasting," Energies, MDPI, vol. 12(23), pages 1-14, November.
    26. Christopher Kath, 2019. "Modeling Intraday Markets under the New Advances of the Cross-Border Intraday Project (XBID): Evidence from the German Intraday Market," Energies, MDPI, vol. 12(22), pages 1-35, November.
    27. Christopher Kath & Florian Ziel, 2018. "The value of forecasts: Quantifying the economic gains of accurate quarter-hourly electricity price forecasts," Papers 1811.08604, arXiv.org.
    28. 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.
    29. Ismail Shah & Faheem Jan & Sajid Ali & Tahir Mehmood, 2022. "Functional Data Approach for Short-Term Electricity Demand Forecasting," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-14, June.
    30. Sergei Kulakov & Florian Ziel, 2019. "Determining Fundamental Supply and Demand Curves in a Wholesale Electricity Market," Papers 1903.11383, arXiv.org, revised Nov 2019.
    31. Micha{l} Narajewski & Florian Ziel, 2020. "Ensemble Forecasting for Intraday Electricity Prices: Simulating Trajectories," Papers 2005.01365, arXiv.org, revised Aug 2020.
    32. Ekaterina Abramova & Derek Bunn, 2020. "Forecasting the Intra-Day Spread Densities of Electricity Prices," Papers 2002.10566, arXiv.org.
    33. 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.
    34. Katarzyna Maciejowska & Weronika Nitka & Tomasz Weron, 2019. "Day-Ahead vs. Intraday—Forecasting the Price Spread to Maximize Economic Benefits," Energies, MDPI, vol. 12(4), pages 1-15, February.
    35. Ekaterina Abramova & Derek Bunn, 2020. "Forecasting the Intra-Day Spread Densities of Electricity Prices," Energies, MDPI, vol. 13(3), pages 1-31, February.
    36. Narajewski, Michał & Ziel, Florian, 2020. "Ensemble forecasting for intraday electricity prices: Simulating trajectories," Applied Energy, Elsevier, vol. 279(C).
    37. 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.
    38. Micha{l} Narajewski & Florian Ziel, 2019. "Estimation and simulation of the transaction arrival process in intraday electricity markets," Papers 1901.09729, arXiv.org, revised Dec 2019.
    39. Koch, Christopher & Hirth, Lion, 2019. "Short-term electricity trading for system balancing: An empirical analysis of the role of intraday trading in balancing Germany's electricity system," Renewable and Sustainable Energy Reviews, Elsevier, vol. 113(C), pages 1-1.
    40. Harvey, David & Leybourne, Stephen & Newbold, Paul, 1997. "Testing the equality of prediction mean squared errors," International Journal of Forecasting, Elsevier, vol. 13(2), pages 281-291, June.
    41. Uniejewski, Bartosz & Weron, Rafał, 2021. "Regularized quantile regression averaging for probabilistic electricity price forecasting," Energy Economics, Elsevier, vol. 95(C).
    42. 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).
    43. Pape, Christian & Hagemann, Simon & Weber, Christoph, 2016. "Are fundamentals enough? Explaining price variations in the German day-ahead and intraday power market," Energy Economics, Elsevier, vol. 54(C), pages 376-387.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Eleni Ntemou & Filippos Ioannidis & Kyriaki Kosmidou & Kostas Andriosopoulos, 2025. "Navigating Electricity Market Design of Greece: Challenges and Reform Initiatives," Energies, MDPI, vol. 18(10), pages 1-22, May.

    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. Narajewski, Michał & Ziel, Florian, 2020. "Ensemble forecasting for intraday electricity prices: Simulating trajectories," Applied Energy, Elsevier, vol. 279(C).
    2. Katarzyna Maciejowska & Bartosz Uniejewski & Rafa{l} Weron, 2022. "Forecasting Electricity Prices," Papers 2204.11735, arXiv.org.
    3. Micha{l} Narajewski & Florian Ziel, 2020. "Ensemble Forecasting for Intraday Electricity Prices: Simulating Trajectories," Papers 2005.01365, arXiv.org, revised Aug 2020.
    4. Michał Narajewski, 2022. "Probabilistic Forecasting of German Electricity Imbalance Prices," Energies, MDPI, vol. 15(14), pages 1-17, July.
    5. Marcjasz, Grzegorz & Narajewski, Michał & Weron, Rafał & Ziel, Florian, 2023. "Distributional neural networks for electricity price forecasting," Energy Economics, Elsevier, vol. 125(C).
    6. Micha{l} Narajewski, 2022. "Probabilistic forecasting of German electricity imbalance prices," Papers 2205.11439, arXiv.org.
    7. Serafin, Tomasz & Marcjasz, Grzegorz & Weron, Rafał, 2022. "Trading on short-term path forecasts of intraday electricity prices," Energy Economics, Elsevier, vol. 112(C).
    8. Narajewski, Michał & Ziel, Florian, 2022. "Optimal bidding in hourly and quarter-hourly electricity price auctions: Trading large volumes of power with market impact and transaction costs," Energy Economics, Elsevier, vol. 110(C).
    9. Micha{l} Narajewski & Florian Ziel, 2021. "Optimal bidding in hourly and quarter-hourly electricity price auctions: trading large volumes of power with market impact and transaction costs," Papers 2104.14204, arXiv.org, revised Feb 2022.
    10. Christopher Kath & Florian Ziel, 2020. "Optimal Order Execution in Intraday Markets: Minimizing Costs in Trade Trajectories," Papers 2009.07892, arXiv.org, revised Oct 2020.
    11. Rainer Baule & Michael Naumann, 2021. "Volatility and Dispersion of Hourly Electricity Contracts on the German Continuous Intraday Market," Energies, MDPI, vol. 14(22), pages 1-24, November.
    12. Li, Wei & Paraschiv, Florentina, 2022. "Modelling the evolution of wind and solar power infeed forecasts," Journal of Commodity Markets, Elsevier, vol. 25(C).
    13. Grzegorz Marcjasz & Bartosz Uniejewski & Rafał Weron, 2020. "Beating the Naïve—Combining LASSO with Naïve Intraday Electricity Price Forecasts," Energies, MDPI, vol. 13(7), pages 1-16, April.
    14. Janczura, Joanna & Wójcik, Edyta, 2022. "Dynamic short-term risk management strategies for the choice of electricity market based on probabilistic forecasts of profit and risk measures. The German and the Polish market case study," Energy Economics, Elsevier, vol. 110(C).
    15. 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).
    16. 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.
    17. Richter, Lucas & Lehna, Malte & Marchand, Sophie & Scholz, Christoph & Dreher, Alexander & Klaiber, Stefan & Lenk, Steve, 2022. "Artificial Intelligence for Electricity Supply Chain automation," Renewable and Sustainable Energy Reviews, Elsevier, vol. 163(C).
    18. Simon Hirsch & Florian Ziel, 2023. "Multivariate Simulation-based Forecasting for Intraday Power Markets: Modelling Cross-Product Price Effects," Papers 2306.13419, arXiv.org.
    19. Christopher Kath & Weronika Nitka & Tomasz Serafin & Tomasz Weron & Przemysław Zaleski & Rafał Weron, 2020. "Balancing Generation from Renewable Energy Sources: Profitability of an Energy Trader," Energies, MDPI, vol. 13(1), pages 1-15, January.
    20. Cramer, Eike & Witthaut, Dirk & Mitsos, Alexander & Dahmen, Manuel, 2023. "Multivariate probabilistic forecasting of intraday electricity prices using normalizing flows," Applied Energy, Elsevier, vol. 346(C).

    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:eee:appene:v:380:y:2025:i:c:s0306261924023596. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/405891/description#description .

    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.