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Multivariate Probabilistic CRPS Learning with an Application to Day-Ahead Electricity Prices

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  • Jonathan Berrisch
  • Florian Ziel

Abstract

This paper presents a new method for combining (or aggregating or ensembling) multivariate probabilistic forecasts, considering dependencies between quantiles and marginals through a smoothing procedure that allows for online learning. We discuss two smoothing methods: dimensionality reduction using Basis matrices and penalized smoothing. The new online learning algorithm generalizes the standard CRPS learning framework into multivariate dimensions. It is based on Bernstein Online Aggregation (BOA) and yields optimal asymptotic learning properties. The procedure uses horizontal aggregation, i.e., aggregation across quantiles. We provide an in-depth discussion on possible extensions of the algorithm and several nested cases related to the existing literature on online forecast combination. We apply the proposed methodology to forecasting day-ahead electricity prices, which are 24-dimensional distributional forecasts. The proposed method yields significant improvements over uniform combination in terms of continuous ranked probability score (CRPS). We discuss the temporal evolution of the weights and hyperparameters and present the results of reduced versions of the preferred model. A fast C++ implementation of the proposed algorithm is provided in the open-source R-Package profoc on CRAN.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2303.10019
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    References listed on IDEAS

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    1. Anne Sofie Jore & James Mitchell & Shaun P. Vahey, 2010. "Combining forecast densities from VARs with uncertain instabilities," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 621-634.
    2. Victor Chernozhukov & Iv·n Fern·ndez-Val & Alfred Galichon, 2010. "Quantile and Probability Curves Without Crossing," Econometrica, Econometric Society, vol. 78(3), pages 1093-1125, May.
    3. 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.
    4. Gneiting, Tilmann, 2011. "Quantiles as optimal point forecasts," International Journal of Forecasting, Elsevier, vol. 27(2), pages 197-207.
    5. 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.
    6. Nowotarski, Jakub & Raviv, Eran & Trück, Stefan & Weron, Rafał, 2014. "An empirical comparison of alternative schemes for combining electricity spot price forecasts," Energy Economics, Elsevier, vol. 46(C), pages 395-412.
    7. Avci, Ezgi & Ketter, Wolfgang & van Heck, Eric, 2018. "Managing electricity price modeling risk via ensemble forecasting: The case of Turkey," Energy Policy, Elsevier, vol. 123(C), pages 390-403.
    8. Simon N. Wood & Zheyuan Li & Gavin Shaddick & Nicole H. Augustin, 2017. "Generalized Additive Models for Gigadata: Modeling the U.K. Black Smoke Network Daily Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1199-1210, July.
    9. Grzegorz Marcjasz & Tomasz Serafin & Rafał Weron, 2018. "Selection of Calibration Windows for Day-Ahead Electricity Price Forecasting," Energies, MDPI, vol. 11(9), pages 1-20, September.
    10. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc4b6ga2g is not listed on IDEAS
    11. Anne Opschoor & Dick van Dijk & Michel van der Wel, 2017. "Combining density forecasts using focused scoring rules," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(7), pages 1298-1313, November.
    12. Bordignon, Silvano & Bunn, Derek W. & Lisi, Francesco & Nan, Fany, 2013. "Combining day-ahead forecasts for British electricity prices," Energy Economics, Elsevier, vol. 35(C), pages 88-103.
    13. 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.
    14. 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.
    15. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4b6ga2g is not listed on IDEAS
    16. Marcjasz, Grzegorz & Narajewski, Michał & Weron, Rafał & Ziel, Florian, 2023. "Distributional neural networks for electricity price forecasting," Energy Economics, Elsevier, vol. 125(C).
    17. 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.
    18. Tu, Jun & Zhou, Guofu, 2011. "Markowitz meets Talmud: A combination of sophisticated and naive diversification strategies," Journal of Financial Economics, Elsevier, vol. 99(1), pages 204-215, January.
    19. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    20. 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.
    21. Gneiting, Tilmann, 2011. "Quantiles as optimal point forecasts," International Journal of Forecasting, Elsevier, vol. 27(2), pages 197-207, April.
    22. 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.
    23. Nowotarski, Jakub & Liu, Bidong & Weron, Rafał & Hong, Tao, 2016. "Improving short term load forecast accuracy via combining sister forecasts," Energy, Elsevier, vol. 98(C), pages 40-49.
    24. 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.
    25. Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007. "Quantile and probability curves without crossing," CeMMAP working papers CWP10/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    26. Chun, Hyonho & Lee, Myung Hee & Fleet, James C. & Oh, Ji Hwan, 2016. "Graphical models via joint quantile regression with component selection," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 162-171.
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    Cited by:

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