IDEAS home Printed from https://ideas.repec.org/a/eee/eneeco/v148y2025ics0140988325004207.html

Loss functions in regression models: Impact on profits and risk in day-ahead electricity trading

Author

Listed:
  • Serafin, Tomasz
  • Weron, Rafał

Abstract

We study the impact of the loss function used to estimate the parameters of a regression-type model on profits and risk in day-ahead electricity trading. To provide practical insights, we consider a strategy that incorporates battery storage and includes realistic operating costs in the calculation of revenues. Using 2021-2024 data from the German market as the testing ground, we provide evidence that minimizing a loss function that combines absolute errors with a quadratic penalty for price spread predictions of the opposite sign is the preferred option. Forecasts based on the introduced directional loss function repeatedly and in the majority of cases yield trading decisions that outperform those based on predictions from models estimated using squared, absolute, percentage, or asymmetric losses, as measured by the Sharpe ratio and profits per trade.

Suggested Citation

  • Serafin, Tomasz & Weron, Rafał, 2025. "Loss functions in regression models: Impact on profits and risk in day-ahead electricity trading," Energy Economics, Elsevier, vol. 148(C).
    • Handle: RePEc:eee:eneeco:v:148:y:2025:i:c:s0140988325004207
    DOI: 10.1016/j.eneco.2025.108596
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0140988325004207
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.eneco.2025.108596?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 look for a different version below or

    for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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).
    2. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    3. Lars Ivar Hagfors & Hilde Hørthe Kamperud & Florentina Paraschiv & Marcel Prokopczuk & Alma Sator & Sjur Westgaard, 2016. "Prediction of extreme price occurrences in the German day-ahead electricity market," Quantitative Finance, Taylor & Francis Journals, vol. 16(12), pages 1929-1948, December.
    4. 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.
    5. 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.
    6. 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.
    7. 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).
    8. Bartosz Uniejewski, 2024. "Regularization for electricity price forecasting," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 34(3), pages 267-286.
    9. 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).
    10. Yael Grushka-Cockayne & Kenneth C. Lichtendahl Jr. & Victor Richmond R. Jose & Robert L. Winkler, 2017. "Quantile Evaluation, Sensitivity to Bracketing, and Sharing Business Payoffs," Operations Research, INFORMS, vol. 65(3), pages 712-728, June.
    11. Narajewski, Michał & Ziel, Florian, 2020. "Econometric modelling and forecasting of intraday electricity prices," Journal of Commodity Markets, Elsevier, vol. 19(C).
    12. Katrzyna Maciejowska, 2022. "Portfolio management of a small RES utility with a structural vector autoregressive model of electricity markets in Germany," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 32(4), pages 75-90.
    13. Gneiting, Tilmann, 2011. "Quantiles as optimal point forecasts," International Journal of Forecasting, Elsevier, vol. 27(2), pages 197-207, April.
    14. 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.
    15. Diamantis Koutsandreas & Evangelos Spiliotis & Fotios Petropoulos & Vassilios Assimakopoulos, 2022. "On the selection of forecasting accuracy measures," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 73(5), pages 937-954, May.
    16. Hyndman, Rob J. & Koehler, Anne B., 2006. "Another look at measures of forecast accuracy," International Journal of Forecasting, Elsevier, vol. 22(4), pages 679-688.
    17. 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.
    18. Tao Hong & Pierre Pinson & Yi Wang & Rafal Weron & Dazhi Yang & Hamidreza Zareipour, 2020. "Energy forecasting: A review and outlook," WORking papers in Management Science (WORMS) WORMS/20/08, Department of Operations Research and Business Intelligence, Wroclaw University of Science and Technology.
    19. Gneiting, Tilmann, 2011. "Quantiles as optimal point forecasts," International Journal of Forecasting, Elsevier, vol. 27(2), pages 197-207.
    20. Ying Chen & Bo Li, 2017. "An Adaptive Functional Autoregressive Forecast Model to Predict Electricity Price Curves," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(3), pages 371-388, July.
    21. Lago, Jesus & De Ridder, Fjo & De Schutter, Bart, 2018. "Forecasting spot electricity prices: Deep learning approaches and empirical comparison of traditional algorithms," Applied Energy, Elsevier, vol. 221(C), pages 386-405.
    22. Maciejowska, Katarzyna & Nowotarski, Jakub, 2016. "A hybrid model for GEFCom2014 probabilistic electricity price forecasting," International Journal of Forecasting, Elsevier, vol. 32(3), pages 1051-1056.
    23. Pesaran, M. Hashem & Pick, Andreas, 2011. "Forecast Combination Across Estimation Windows," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(2), pages 307-318.
    24. Elizabeth Yardley & Fotios Petropoulos, 2021. "Beyond Error Measures to the Utility and Cost of the Forecasts," Foresight: The International Journal of Applied Forecasting, International Institute of Forecasters, issue 63, pages 36-45, Q4.
    25. Lisi, Francesco & Pelagatti, Matteo M., 2018. "Component estimation for electricity market data: Deterministic or stochastic?," Energy Economics, Elsevier, vol. 74(C), pages 13-37.
    26. 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.
    27. Kuppelwieser, Thomas & Wozabal, David, 2021. "Liquidity costs on intraday power markets: Continuous trading versus auctions," Energy Policy, Elsevier, vol. 154(C).
    28. 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).
    29. Ekaterina Abramova & Derek Bunn, 2020. "Forecasting the Intra-Day Spread Densities of Electricity Prices," Papers 2002.10566, arXiv.org.
    30. Maciejowska, Katarzyna, 2020. "Assessing the impact of renewable energy sources on the electricity price level and variability – A quantile regression approach," Energy Economics, Elsevier, vol. 85(C).
    31. 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).
    32. 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).
    33. 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).
    34. Raffaella Giacomini & Barbara Rossi, 2013. "Forecasting in macroeconomics," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 17, pages 381-408, Edward Elgar Publishing.
    35. Tomasz Sikorski & Michał Jasiński & Edyta Ropuszyńska-Surma & Magdalena Węglarz & Dominika Kaczorowska & Paweł Kostyła & Zbigniew Leonowicz & Robert Lis & Jacek Rezmer & Wilhelm Rojewski & Marian Sobi, 2019. "A Case Study on Distributed Energy Resources and Energy-Storage Systems in a Virtual Power Plant Concept: Economic Aspects," Energies, MDPI, vol. 12(23), pages 1-21, November.
    36. Ekaterina Abramova & Derek Bunn, 2020. "Forecasting the Intra-Day Spread Densities of Electricity Prices," Energies, MDPI, vol. 13(3), pages 1-31, February.
    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. Gaillard, Pierre & Goude, Yannig & Nedellec, Raphaël, 2016. "Additive models and robust aggregation for GEFCom2014 probabilistic electric load and electricity price forecasting," International Journal of Forecasting, Elsevier, vol. 32(3), pages 1038-1050.
    39. 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.
    40. Katarzyna Maciejowska, 2022. "A portfolio management of a small RES utility with a Structural Vector Autoregressive model of German electricity markets," Papers 2205.00975, arXiv.org.
    41. Davydenko, Andrey & Fildes, Robert, 2013. "Measuring forecasting accuracy: The case of judgmental adjustments to SKU-level demand forecasts," International Journal of Forecasting, Elsevier, vol. 29(3), pages 510-522.
    42. Uniejewski, Bartosz & Weron, Rafał, 2021. "Regularized quantile regression averaging for probabilistic electricity price forecasting," Energy Economics, Elsevier, vol. 95(C).
    43. Joanna Janczura, 2025. "Expectile regression averaging method for probabilistic forecasting of electricity prices," Computational Statistics, Springer, vol. 40(2), pages 683-700, February.
    44. Katarzyna Maciejowska & Tomasz Serafin & Bartosz Uniejewski, 2023. "Probabilistic forecasting with a hybrid Factor-QRA approach: Application to electricity trading," Papers 2303.08565, arXiv.org, revised Nov 2024.
    45. Marcjasz, Grzegorz & Narajewski, Michał & Weron, Rafał & Ziel, Florian, 2023. "Distributional neural networks for electricity price forecasting," Energy Economics, Elsevier, vol. 125(C).
    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. Arkadiusz Lipiecki & Kaja Bilinska & Nikolaos Kourentzes & Rafal Weron, 2025. "Stealing accuracy: Predicting day-ahead electricity prices with Temporal Hierarchy Forecasting (THieF)," WORking papers in Management Science (WORMS) WORMS/25/06, Department of Operations Research and Business Intelligence, Wroclaw University of Science and Technology.
    2. Katarzyna Maciejowska & Arkadiusz Lipiecki & Bartosz Uniejewski, 2025. "Statistical and economic evaluation of forecasts in electricity markets: beyond RMSE and MAE," Papers 2511.13616, arXiv.org, revised Mar 2026.

    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. 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).
    2. Katarzyna Maciejowska & Bartosz Uniejewski & Rafa{l} Weron, 2022. "Forecasting Electricity Prices," Papers 2204.11735, arXiv.org.
    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. Marcjasz, Grzegorz & Narajewski, Michał & Weron, Rafał & Ziel, Florian, 2023. "Distributional neural networks for electricity price forecasting," Energy Economics, Elsevier, vol. 125(C).
    5. Uniejewski, Bartosz, 2025. "Smoothing quantile regression averaging: A new approach to probabilistic forecasting of electricity prices," Journal of Commodity Markets, Elsevier, vol. 39(C).
    6. 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).
    7. Bartosz Uniejewski, 2023. "Smoothing Quantile Regression Averaging: A new approach to probabilistic forecasting of electricity prices," Papers 2302.00411, arXiv.org, revised Nov 2024.
    8. Uniejewski, Bartosz & Weron, Rafał, 2021. "Regularized quantile regression averaging for probabilistic electricity price forecasting," Energy Economics, Elsevier, vol. 95(C).
    9. Bartosz Uniejewski, 2024. "Regularization for electricity price forecasting," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 34(3), pages 267-286.
    10. 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.
    11. 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).
    12. Katarzyna Maciejowska & Weronika Nitka, 2024. "Multiple split approach -- multidimensional probabilistic forecasting of electricity markets," Papers 2407.07795, arXiv.org.
    13. Serafin, Tomasz & Marcjasz, Grzegorz & Weron, Rafał, 2022. "Trading on short-term path forecasts of intraday electricity prices," Energy Economics, Elsevier, vol. 112(C).
    14. 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.
    15. Narajewski, Michał & Ziel, Florian, 2020. "Ensemble forecasting for intraday electricity prices: Simulating trajectories," Applied Energy, Elsevier, vol. 279(C).
    16. Nickelsen, Daniel & Müller, Gernot, 2025. "Bayesian hierarchical probabilistic forecasting of intraday electricity prices," Applied Energy, Elsevier, vol. 380(C).
    17. Ciaran O'Connor & Mohamed Bahloul & Steven Prestwich & Andrea Visentin, 2025. "The Evolution of Probabilistic Price Forecasting Techniques: A Review of the Day-Ahead, Intra-Day, and Balancing Markets," Papers 2511.05523, arXiv.org.
    18. Hanus, Luboš & Baruník, Jozef, 2025. "Learning the probability distributions of day-ahead electricity prices," Energy Economics, Elsevier, vol. 152(C).
    19. Michał Narajewski, 2022. "Probabilistic Forecasting of German Electricity Imbalance Prices," Energies, MDPI, vol. 15(14), pages 1-17, July.
    20. Marcjasz, Grzegorz & Uniejewski, Bartosz & Weron, Rafał, 2020. "Probabilistic electricity price forecasting with NARX networks: Combine point or probabilistic forecasts?," International Journal of Forecasting, Elsevier, vol. 36(2), pages 466-479.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • Q41 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Demand and Supply; Prices
    • Q47 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Energy Forecasting

    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:eee:eneeco:v:148:y:2025:i:c:s0140988325004207. 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/locate/eneco .

    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.