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As global warming intensifies, the reduction of carbon emissions is imminent. Carbon price is directly related to whether carbon can be effectively reduced. Therefore, accurately forecasting carbon price has important practical significance. Aiming at the nonstationary and nonlinear characteristics of carbon price, this paper proposes a novel hybrid model for forecasting carbon price, which is based on improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), multiscale fuzzy entropy (MFE), complete ensemble empirical mode decomposition (CEEMD), improved random forest by salp swarm algorithm (SSARF), improved back propagation by cuckoo search (CSBP), improved extreme learning machine by whale optimization algorithm (WOAELM) and error correction (EC), named ICEEMDAN-MFE-CEEMD-SSARF-CSBP-WOAELM-EC. Firstly, carbon price is decomposed by ICEEMDAN, divided into high-, medium-, and low-complexity components by MFE. Secondly, high-complexity components are merged and secondarily decomposed by CEEMD, which are still recorded as high-complexity components. Then, SSARF, CSBP and WOAELM are used to forecast high-, medium-, and low-complexity components, respectively, and forecasting results are reconstructed. Finally, EC is carried out using an extreme learning machine to obtain the final forecasting results, and the Diebold-Mariano test is introduced for a comprehensive evaluation of the model. Taking carbon price in the pilot cities of Shenzhen and Hubei as examples, after 6 aspects and 20 comparative experiments, the results show that the proposed model has higher forecast accuracy, with MAPE, MAE and RMSE up to 0.03131, 0.00089 and 4.02e-06 in Hubei, and its forecasting ability is better than other commonly used international carbon financial price forecasting models, providing a theoretical and data basis for carbon pricing and formulating carbon reduction policies in China. The main contributions of this paper are the improved primary decomposition, the use of secondary decomposition, and the innovative combination of three optimal models to forecast carbon price, but it still needs to be optimized for practice. [Display omitted] • Propose improve CEEMDAN by using Hermite interpolation and calculating residuals first. • High complexity components are secondarily decomposed to reduce its complexity. • Improved RF by SSA, named SSARF, is proposed to solve the dilemmas of RF. • Propose a high-accuracy hybrid model for carbon price forecasting. • Compare multi-faceted experiments to prove the validity of the proposed model. [ABSTRACT FROM AUTHOR]