As a central participant and important leader in the global climate governance system, China is facing the urgent need to predict and regulate the price of carbon emissions to promote the sound development of its carbon market. In this article, a rolling prediction model based on Least Absolute Shrinkage and Selection Operator-cheetah optimization algorithm-extreme gradient boosting (Lasso-COA-XGBoost) carbon price decomposition integration is proposed to address the defects of low prediction accuracy and insufficient model stability of a single machine learning model in the carbon price prediction problem. During the modeling process, the adaptive Lasso method is first employed to select factors from 15 primary indicators of carbon prices, identifying the most important influencing factors. Next, the COA-XGBoost model is built and the parameters of the XGBoost model are optimized using the COA algorithm. Finally, the complete ensemble empirical Mode Decomposition with adaptive noise (CEEMDAM) method is utilized to decompose the residual sequence of the COA-XGBoost model and reconstruct it into high-frequency and low-frequency components. Appropriate frequency models are applied to achieve error correction, thereby constructing the combined Lasso-COA-XGBoost-CEEMDAN model. To further enhance the predictive accuracy and practicality of the model, a rolling time window is introduced for forecasting in the Hubei and Guangzhou carbon emission trading markets, ensuring that the forecasting model can adapt to market changes in real-time. The experimental results show that, taking the carbon price prediction in Hubei as an example, the proposed hybrid model has a significant improvement in prediction accuracy compared with the comparison model (XGBoost model): the RMSE is improved by 99.9987%, the MAE is improved by 99.9039%, the MAPE is improved by 99.9960%, and the R is improved by 0.2004%, and the advantages of this hybrid model are also verified in other experiments. The results provide an effective experimental method for future carbon price prediction.