An optimal multi-scale and multi-factor two-stage integration paradigm coupled with investor sentiment for carbon price prediction

•An optimal multi-scale and multi-factor two-stage integration paradigm coupled with investor sentiment is designed for carbon price prediction.•The adaptive periodic variational mode decomposition algorithm is proposed to fully capture the optimal fluctuation characteristics of carbon price data.•A comprehensive impact factor library is constructed to assist forecasting, including unstructured data on investor sentiment and structured data.•A comprehensive feature factor screening framework is constructed to capture the optimal driving factors.•An optimal two-stage integration prediction system is developed to achieve high accuracy prediction. The accurate prediction of carbon emission trading prices is of great significance for the effective allocation of carbon resources, achieving energy conservation, emission reduction, and green development. However, it is difficult to fully extract the fluctuation information of carbon price, and external factors also have complex impacts on it, so it is a challenge to accurately predict carbon price. Therefore, this study proposes an optimal multi-scale and multi-factor two-stage integration paradigm coupled with investor sentiment for carbon price prediction. Firstly, an adaptive periodic variational mode decomposition (APVMD) method is proposed to capture feature subsequences with different fluctuation information from a periodic perspective in carbon prices. Then a comprehensive impact factor library is constructed to assist in prediction, including unstructured data on investor sentiment and structured data. Through the enhanced light gradient boosting machine (ELightGBM) algorithm, the optimal driving factors for each feature subsequence are fully screened, and the dimensionality of the data is reduced based on their nonlinear relationship. Considering the selection of hyperparameters and the contribution of different feature subsequences, an optimized two-stage integrated prediction is designed to achieve high-precision point prediction. On this basis, uncertainty analysis is used to obtain reasonable interval prediction results. Through comparative analysis, this model is better than other comparative models in terms of predictive ability and stability.