Abbreviations of professional terms.

An accurate prediction of carbon pricing is essential in carbon emission management, and also provides an important role for governments to formulate corresponding policies. However, due to the inherent complexity and dynamics of carbon price sequence, the effectiveness of different decomposition algorithms for carbon price remains to be tested. In addition, existing studies lack a systematic framework to explore the organic integration of external factors and secondary decomposition technology, and the feature processing of complex external factors still needs to be improved. In order to overcome the shortcomings of existing research, This paper presents a Variational Modal Decomposition(VMD) algorithm and a Complete Ensemble Empirical Mode Decomposition with Adaptive Second decomposition technology of Noise(CEEMDAN) decomposition algorithm, and extract the features of external factors by Extreme Gradient Boosting (XGBoost) algorithm. The HI-VMD-PE-CEEMDAN-XGBoost-Transformer model for predicting carbon price is constructed by the combined Transformer algorithm. Specifically, first, we use Hampel identifer(HI) to detect and rectify the anomalies in the original sequence. After applying Variational Mode Decomposition(VMD) decomposition algorithm, Permutation Entropy(PE) is utilized to reassemble the decomposed component. Quadratic Decomposition is performed by Complete Ensemble Empirical Mode Decomposition with Adaptive Noise(CEEMDAN) algorithm. Then, the XGBoost algorithm is employed to extract features of external factors and screen key factors as predictive input variables. Finally, Transformer, which has stronger capability of large-scale data parallel processing, is selected as the prediction model to achieve a more scientific and effective carbon price prediction. The empirical analysis results based on EU carbon market data verify the validity and superiority of the proposed model in different forecasting scenarios.精准预测碳定价在碳排放管理中至关重要，同时也为政府制定相应政策提供重要支撑。然而，由于碳价格序列固有的复杂性与动态性，不同分解算法在碳价格预测中的有效性仍有待验证。此外，现有研究缺乏系统性框架以探索外部因素与二次分解技术的有机融合，复杂外部因素的特征处理仍有待完善。为克服现有研究的不足，本文提出结合变分模态分解（Variational Modal Decomposition, VMD）算法与自适应噪声完备集合经验模态分解（Complete Ensemble Empirical Mode Decomposition with Adaptive Noise, CEEMDAN）的二次分解技术，并通过极限梯度提升（Extreme Gradient Boosting, XGBoost）算法提取外部因素特征。结合Transformer算法构建了HI-VMD-PE-CEEMDAN-XGBoost-Transformer碳价格预测模型。具体而言，首先利用汉普尔标识符（Hampel identifer, HI）检测并修正原始序列中的异常值；经变分模态分解（VMD）算法分解后，采用排列熵（Permutation Entropy, PE）对分解得到的分量进行重组；随后通过自适应噪声完备集合经验模态分解（CEEMDAN）算法完成二次分解；接着利用XGBoost算法提取外部因素特征并筛选关键因子作为预测输入变量；最后选用具备更强大规模数据并行处理能力的Transformer作为预测模型，以实现更科学高效的碳价格预测。基于欧盟碳市场数据的实证分析结果验证了所提模型在不同预测场景下的有效性与优越性。