Forecasting the Carbon Price Using Extreme-Point Symmetric Mode Decomposition and Extreme Learning Machine Optimized by the Grey Wolf Optimizer Algorithm

Due to the nonlinear and non-stationary characteristics of the carbon price, it is difficult to predict the carbon price accurately. This paper proposes a new novel hybrid model for carbon price prediction. The proposed model consists of an extreme-point symmetric mode decomposition, an extreme learning machine, and a grey wolf optimizer algorithm. Firstly, the extreme-point symmetric mode decomposition is employed to decompose the carbon price into several intrinsic mode functions and one residue. Then, the partial autocorrelation function is utilized to determine the input variables of the intrinsic mode functions, and the residue of the extreme learning machine. In the end, the grey wolf optimizer algorithm is applied to optimize the extreme learning machine, to forecast the carbon price. To illustrate the superiority of the proposed model, the Hubei, Beijing, Shanghai, and Guangdong carbon price series are selected for the predictions. The empirical results confirm that the proposed model is superior to the other benchmark methods. Consequently, the proposed model can be employed as an effective method for carbon price series analysis and forecasting.