Modelling of carbon price in two real carbon trading markets

Abstract

Abstract 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.