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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]

Carbon price forecasting plays a vital role in establishing a reasonable and stable carbon market. A number of carbon price forecasting models have been developed to improve the effectiveness of the predictions. However, most of the previous studies failed to focus on the role of choosing the appropriate input features and only aimed to improve the forecasting accuracy. In this paper, a novel hybrid model based on feature selection and a multi-objective optimization algorithm is proposed for carbon price forecasting. More specifically, the main novel contributions of this study are as follows. A two-stage feature selection method is developed to obtain the appropriate input variables to enhance the forecasting ability. In addition, the weighted regularized extreme learning machine is optimized using a multi-objective optimization algorithm, named the multi-objective grasshopper optimization algorithm, which can obtain better forecasting results. To demonstrate the effectiveness of the developed carbon price forecasting model, two daily carbon price datasets that were collected from the China and European Union Emissions Trading Scheme, are used in this study. The results revealed that the mean absolute percentage errors of the proposed model utilizing data from the China and European Union Emissions Trading Scheme are 2.4923% and 0.8418%, respectively, which are lower than those of other compared models. In addition, the variances of the forecasting errors of the developed model are 1.1419 and 0.0038 for the data from the China and European Union Emissions Trading Scheme, respectively. These results reflect the superior forecasting ability of this method compared to other methods. Therefore, the proposed method is more effective than other models in carbon price forecasting. • A novel hybrid forecasting architecture is proposed for carbon price forecasting. • A two-stage feature selection method is proposed to gain optimal input variables. • A multi-objective optimization algorithm is used to improve the prediction results. • The developed model can perform better using both EU ETS and China data. [ABSTRACT FROM AUTHOR]