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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]

Motivated by reducing carbon emissions, carbon trading market have been opened to promote environmental protection. Accurate carbon trading volume and price forecasts have far-reaching implications for environmental and energy policy formulation. As the country with the most massive carbon emissions in the world, China's carbon price trends, carbon trading volume trends, and policy orientation are of great significance. As matters stand, there are few studies on carbon price and trading volume forecasts, and no research paper has covered carbon price and trading volume forecasts for all carbon trading markets in China. In order to provide a relatively complete reference for the carbon price and trading volume in China, this paper uses six machine learning models to predict the daily carbon price and trading volume of eight carbon markets in China, including Beijing, Shenzhen, Guangdong, Hubei, Shanghai, Fujian, Tianjin, Chongqing. The prediction models include extreme gradient boosting, random forest, kernel-based nonlinear extension of the Arps decline model optimized by grey wolf optimizer (GWO-KNEA), support vector machine optimized by particle swarm optimizer, support vector machine optimized by fruit fly optimizer and simulated annealing algorithm, and radial basis function neural network (RBFNN). Moreover, an advanced data denoising method, i.e., complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), is used in the models to smooth the raw data. Because the eight carbon trading markets have different carbon price and trading volume distribution characteristics in time series, by comparing the prediction results, more suitable models for the specific carbon market can be obtained. The prediction results show that CEEMDAN-GWO-KNEA and CEEMDAN-RBFNN are more competitive in predicting carbon prices and trading volume in China because of their best performance in many datasets. The average accuracy of CEEMDAN-RBFNN and CEMDAN-GWO-KNEA in carbon price prediction is 98.40% and 97.89%, respectively. The predictive stability of each model in different application scenarios is also discussed. The results show that high prediction accuracy does not mean better prediction stability, but CEEMDAN-RBFNN and CEMDAN-GWO-KNEA can still guarantee high stability in most datasets. [ABSTRACT FROM AUTHOR]