Jonathan Berrisch, Florian Ziel
arXiv 1 Feb 2021 · Statistics — Machine Learning
arXiv:2102.00968 · PDF · Extracted main text
Combination and aggregation techniques can significantly improve forecast accuracy. This also holds for probabilistic forecasting methods where predictive distributions are combined. There are several time-varying and adaptive weighting schemes such as Bayesian model averaging (BMA). However, the quality of different forecasts may vary not only over time but also within the distribution. For example, some distribution forecasts may be more accurate in the center of the distributions, while others are better at predicting the tails. Therefore, we introduce a new weighting method that considers the differences in performance over time and within the distribution. We discuss pointwise combination algorithms based on aggregation across quantiles that optimize with respect to the continuous ranked probability score (CRPS). After analyzing the theoretical properties of pointwise CRPS learning, we discuss B- and P-Spline-based estimation techniques for batch and online learning, based on quantile regression and prediction with expert advice. We prove that the proposed fully adaptive Bernstein online aggregation (BOA) method for pointwise CRPS online learning has optimal convergence properties. They are confirmed in simulations and a probabilistic forecasting study for European emission allowance (EUA) prices.
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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 | Wintenberger, O (2017) Optimal learning with Bernstein online aggregation | 0.971 | 12 | 4 | 92% |
| 2 | Gaillard, P., Stoltz, G., & Van Erven, T (2014) A second-order bound with excess losses | 0.928 | 4 | 3 | 100% |
| 3 | Cesa-Bianchi, N., & Lugosi, G (2006) Prediction, learning, and games | 0.874 | 8 | 2 | 100% |
| 4 | Thorey, J., Chaussin, C., & Mallet, V (2018) Ensemble forecast of photovoltaic power with online CRPS learning | 0.843 | 3 | 3 | 100% |
| 5 | Gneiting, T (2011) Making and evaluating point forecasts | 0.737 | 3 | 2 | 100% |
| 6 | Raftery, A. E., Gneiting, T., Balabdaoui, F., & Polakowski, M (2005) Using Bayesian Model Averaging to Calibrate Forecast Ensembles | 0.737 | 3 | 2 | 100% |
| 7 | Zamo, M., Bel, L., & Mestre, O (2021) Sequential aggregation of probabilistic forecasts—Application to wind speed ensemble forecasts | 0.737 | 3 | 2 | 100% |
| 8 | Gaillard, P., & Wintenberger, O (2018) Efficient online algorithms for fast-rate regret bounds under sparsity | 0.693 | 6 | 2 | 50% |
| 9 | Aastveit, K. A., Gerdrup, K. R., Jore, A. S., & Thorsrud, L. A (2014) Nowcasting GDP in real time: A density combination approach | 0.644 | 2 | 2 | 100% |
| 10 | Aastveit, K. A., Mitchell, J., Ravazzolo, F., & van Dijk, H. K (2019) The Evolution of Forecast Density Combinations in Economics | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 77 scored citations.