Abstract: Amid the rapid development of global carbon markets, accurate carbon price prediction holds significant importance for policy formulation and market regulation. However, carbon prices are influenced by multiple factors, exhibiting strong volatility and nonlinear characteristics, which pose considerable challenges to forecasting. This paper proposes an ensemble carbon price forecasting model based on a VMD-SWD secondary decomposition framework. First, the Variational Mode Decomposition (VMD), optimized by a Hiking Optimization Algorithm, is employed for primary decomposition of the carbon price series. Subsequently, the residual sequence undergoes secondary decomposition using Swarm Decomposition (SWD) to fully extract effective information and reduce sequence complexity. Next, the decomposed components are reconstructed into low-frequency, medium-frequency, and high-frequency components based on permutation entropy, with differentiated input feature strategies applied to each component. Finally, an optimal predictor selection module incorporating five machine learning models is constructed, and ensemble is achieved through Deep Kernel Extreme Learning Machine. Experiments conducted on data from Hubei, Shanghai, and Fujian carbon markets demonstrate that the proposed model outperforms comparative models in metrics such as MAE and RMSE, validating its effectiveness and robustness. The proposed model not only addresses the dual limitations of VMD but also significantly enhances the model's ability to capture multi-scale features of carbon price series.

Key words: carbon trading price, secondary decomposition, machine learning, forecasting, decomposition-ensemble