Method for predicting the price of carbon based on quadratic decomposition and multiscale prediction

Establishing an effective carbon price forecasting model is crucial for promoting the stable development and effective management of carbon trading markets. To enhance forecasting accuracy, this study proposes a hybrid carbon price prediction model based on secondary decomposition and multi-scale forecasting. First, a WOA-XGBoost model is constructed for the initial carbon price prediction. Then, the residuals of the initial prediction are decomposed using Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), and the component with the highest fuzzy entropy (IMF1) is further decomposed using Variational Mode Decomposition (VMD). The residual components are then reorganized based on their frequency characteristics. Subsequently, different explanatory variables are introduced to model the high- and low-frequency sequences separately. Finally, the prediction results of each sequence are aggregated to obtain the final composite forecast of carbon prices.The results show that: (1) compared with benchmark models, the proposed hybrid model achieves the best overall forecasting performance, with MAE values of 0.0006 and 0.0013 and R² values of 0.9999 in the Hubei and EU carbon markets, respectively; (2) historical carbon prices are the most influential factor in carbon price forecasting. The Baidu Index contributes most significantly in the Hubei market, while the German DAX index has the greatest impact on the EU carbon market. This model framework provides high-precision quantitative support for carbon allowance pricing, policy evaluation, and cross-market linkage analysis, thereby facilitating the transition of carbon markets toward refined governance and global coordinated emission reduction, and promoting green and sustainable development.