标题： 电力价格预测不确定性量化中的等距分位数回归平均法 显示英文标题

标题： Isotonic Quantile Regression Averaging for uncertainty quantification of electricity price forecasts

摘要： 量化预测模型的不确定性对于评估和减轻与数据驱动决策相关的风险至关重要，尤其是在电力市场等波动性较高的领域。 机器学习方法可以提供高度准确的电价预测，这对市场参与者的决策至关重要。 然而，这些模型通常缺乏不确定性估计，这限制了决策者避免不必要的风险的能力。 在本文中，我们提出了一种从点预测集合中生成概率预测的新方法，称为等距分位数回归平均（iQRA）。 在已建立的分位数回归平均（QRA）框架基础上，我们引入了随机序约束，以提高预测准确性、可靠性和计算成本。 在对德国日前电力市场的广泛预测研究中，我们展示了iQRA在可靠性和平滑性方面始终优于最先进的后处理方法。 它在多个置信水平上产生了校准良好的预测区间，相对于所有基准方法，特别是基于覆盖率的共形预测，提供了更优的可靠性。 此外，等距正则化降低了分位数回归问题的复杂性，并提供了一种无需超参数的选择变量方法。 显示英文摘要

摘要： Quantifying the uncertainty of forecasting models is essential to assess and mitigate the risks associated with data-driven decisions, especially in volatile domains such as electricity markets. Machine learning methods can provide highly accurate electricity price forecasts, critical for informing the decisions of market participants. However, these models often lack uncertainty estimates, which limits the ability of decision makers to avoid unnecessary risks. In this paper, we propose a novel method for generating probabilistic forecasts from ensembles of point forecasts, called Isotonic Quantile Regression Averaging (iQRA). Building on the established framework of Quantile Regression Averaging (QRA), we introduce stochastic order constraints to improve forecast accuracy, reliability, and computational costs. In an extensive forecasting study of the German day-ahead electricity market, we show that iQRA consistently outperforms state-of-the-art postprocessing methods in terms of both reliability and sharpness. It produces well-calibrated prediction intervals across multiple confidence levels, providing superior reliability to all benchmark methods, particularly coverage-based conformal prediction. In addition, isotonic regularization decreases the complexity of the quantile regression problem and offers a hyperparameter-free approach to variable selection.