Jonathan Berrisch, Florian Ziel
arXiv 17 Mar 2023 · Statistics — Machine Learning · publishedInternational Journal of Forecasting (2024) · 17 citations (OpenAlex)
arXiv:2303.10019 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Berrisch, J., & Ziel, F (2021) CRPS learning self | 1.000 | 7 | 4 | 100% |
| 2 | Marcjasz, G., Narajewski, M., Weron, R., & Ziel, F (2023) Distributional neural networks for electricity price forecasting self | 0.894 | 7 | 3 | 71% |
| 3 | Cesa-Bianchi, N., & Lugosi, G (2006) Prediction, learning, and games | 0.874 | 5 | 2 | 100% |
| 4 | Berrisch, J., & Ziel, F (2023) The profoc Package: An R package for probabilistic forecast combination self | 0.843 | 3 | 3 | 100% |
| 5 | Dalalyan, A. S., Salmon, J. et al (2012) Sharp oracle inequalities for aggregation of affine estimators | 0.644 | 2 | 2 | 100% |
| 6 | Nitka, W., & Weron, R (2023) Combining predictive distributions of electricity prices. Does minimizing the CRPS lead to optimal decisions in day-ahead bidding? | 0.644 | 2 | 2 | 100% |
| 7 | Wintenberger, O (2017) Optimal learning with bernstein online aggregation | 0.644 | 2 | 2 | 100% |
| 8 | Christoffersen, P. F (1998) Evaluating interval forecasts | 0.511 | 2 | 2 | 50% |
| 9 | Bordignon, S., Bunn, D. W., Lisi, F., & Nan, F (2013) Combining day-ahead forecasts for british electricity prices | 0.511 | 2 | 1 | 100% |
| 10 | Cesa-Bianchi, N., Gaillard, P., Lugosi, G., & Stoltz, G (2012) Mirror descent meets fixed share (and feels no regret) | 0.511 | 2 | 1 | 100% |
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