In this paper, we consider the problem of online probabilistic time series forecasting. The difference between a probabilistic prediction (distribution function) and a numerical outcome is measured using a loss function (scoring rule). In practical statistics, the Continuous Ranked Probability Score (CRPS) rule is often used to estimate the discrepancy between probabilistic predictions and quantitative outcomes. Here, we consider the case when several competing methods (experts) give their predictions in the form of distribution functions. Expert predictions are provided with confidence levels. We propose an algorithm for online aggregation of these distribution functions with allowance for the confidence levels to expert forecasts. The discounted error of the proposed algorithm with allowance for the confidence levels is estimated in the form of a comparison of the cumulative losses of the algorithm and the losses of experts. A technology for constructing predictive expert algorithms and aggregating their probabilistic predictions using the example of the problem of predicting electricity consumption 1 or more hours ahead was developed. The results of numerical experiments using real data are presented.

在本文中，我们考虑了在线概率时间序列预测的问题。概率预测（分布函数）和数值结果之间的差异是使用损失函数（评分规则）来衡量的。在实际统计中，连续排名概率分数 (CRPS) 规则通常用于估计概率预测和定量结果之间的差异。在这里，我们考虑几种竞争方法（专家）以分布函数的形式给出预测的情况。专家预测带有置信度。我们提出了一种在线聚合这些分布函数的算法，并允许专家预测的置信水平。以算法的累积损失和专家损失的比较的形式估计所提出的算法在置信水平允许的情况下的贴现误差。开发了一种技术，用于构建预测专家算法并使用提前 1 小时或更多小时预测电力消耗问题的示例来聚合其概率预测。给出了使用真实数据的数值实验结果。