We study the prices of European Emission Allowances (EUA), whereby we analyze their uncertainty and dependencies on related energy prices (natural gas, coal, and oil). We propose a probabilistic multivariate conditional time series model with a VECM-Copula-GARCH structure which exploits key characteristics of the data. Data are normalized with respect to inflation and carbon emissions to allow for proper cross-series evaluation. The forecasting performance is evaluated in an extensive rolling-window forecasting study, covering eight years out-of-sample. We discuss our findings for both levels- and log-transformed data, focusing on time-varying correlations, and in view of the Russian invasion of Ukraine.

翻译：本研究以欧洲碳排放配额（EUA）为研究对象，系统分析其不确定性及其与相关能源价格（天然气、煤炭与石油）之间的依赖关系。我们构建了一个基于VECM-Copula-GARCH结构的概率性多元条件时间序列模型，该模型充分利用了数据的关键特征。通过通胀与碳排放标准化处理数据，以实现跨序列的合理评估。在涵盖八年样本外数据的滚动窗口预测研究中，我们评估了模型的预测性能。基于原始数据和对数变换数据，我们重点探讨了时变相关性及其在俄乌冲突背景下的动态演变特征。