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A significant milestone in China's carbon market was reached with the official launch and operation of the National Carbon Emission Trading Market. The accurate prediction of the carbon price in this market is crucial for the government to formulate scientific policies regarding the carbon market and for companies to participate effectively. Nevertheless, it remains challenging to accurately predict price fluctuations in the carbon market because of the volatility and instability caused by several complex factors. This paper proposes a new carbon price forecasting framework that considers the potential factors influencing national carbon prices, including data decomposition and reconstruction techniques, feature selection techniques, machine learning forecasting techniques for intelligent optimisation, and research on model interpretability. This comprehensive framework aims to improve the accuracy and understandability of carbon price projections to respond better to the complexity and uncertainty of carbon markets. The results indicate that (1) the hybrid forecasting framework is highly accurate in forecasting national carbon market prices and far superior to other comparative models; (2) the factors driving national carbon prices vary according to the time scale. High-frequency series are sensitive to short-term economic and energy market indicators. Medium- and low-frequency series are more susceptible to financial markets and long-term economic conditions than high-frequency series. This study provides insights into the factors affecting China's national carbon market price and serves as a reference for companies and governments to develop carbon price forecasting tools. • A hybrid carbon price prediction model named FS-CEEMDAN-VMD-GWO-LightGBM is proposed. • Accurately predicted the national carbon price in China using multi-influence factor time series data. • Using a data decomposition and reconstruction strategy, the model's accuracy was improved. • The SHAP algorithm is used to assess the impact of various influencing factors on the fluctuations of carbon prices. [ABSTRACT FROM AUTHOR]