CRPS 学习 (CRPS Learning)

Combination and aggregation techniques can improve forecast accuracy substantially. This also holds for probabilistic forecasting methods where full predictive distributions are combined. There are several time-varying and adaptive weighting schemes like Bayesian model averaging (BMA). However, the performance of different forecasters may vary not only over time but also in parts of the distribution. So one may be more accurate in the center of the distributions, and other ones perform better in predicting the distribution's tails. Consequently, we introduce a new weighting procedure that considers both varying performance across time and the distribution. We discuss pointwise online aggregation algorithms that optimize with respect to the continuous ranked probability score (CRPS). After analyzing the theoretical properties of a fully adaptive Bernstein online aggregation (BOA) method, we introduce smoothing procedures for pointwise CRPS learning. The properties are confirmed and discussed using simulation studies. Additionally, we illustrate the performance in a forecasting study for carbon markets. In detail, we predict the distribution of European emission allowance prices.

翻译：组合和汇总技术可以大幅提高预测的准确性。这还有利于预测预测预测方法, 将完全的预测分布结合起来。有好几种时间和适应性加权方法, 如巴伊西亚模型(BMA 平均 ) 。但是, 不同的预测者的表现可能不仅随时间而变化, 而且在分布过程中的某些部分也不同。因此, 在分布中心, 其他人的特性可能更准确, 而在预测分布尾巴方面表现更好。因此, 我们引入一种新的加权程序, 既考虑不同时间和分布的性能。我们讨论一些有分寸的在线汇总算法, 以优化连续的排名概率分数(CRPS ) 。在分析完全适应的伯恩斯坦在线汇总方法的理论属性之后, 我们引入了通畅的程序, 用于点准CRPS 学习。这些属性通过模拟研究得到确认和讨论。此外, 我们用碳市场预测研究的绩效来说明。我们详细预测欧洲排放允许价格的分布情况。