CRPS Learning
arXiv:2102.00968 · doi:10.1016/j.jeconom.2021.11.008
Abstract
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.
Accepted for publication in Journal of Econometrics
References in corpus (5)
Cited by in corpus (5)
- A review of predictive uncertainty estimation with machine learning
- Distributional Modeling and Forecasting of Natural Gas Prices
- Smoothed Bernstein Online Aggregation for Day-Ahead Electricity Demand Forecasting
- Postprocessing of point predictions for probabilistic forecasting of day-ahead electricity prices: The benefits of using isotonic distributional regression
- Improving probabilistic forecasts of extreme wind speeds by training statistical post-processing models with weighted scoring rules