Profiles of all models.

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.