Preprocessing and postprocessing strategies comparisons: case study of forecasting the carbon price in China.

The accurate carbon price prediction is of significance to decrease investment risks, make scientific decisions and improve production efficiency. As matters stand, most studies focusing on carbon price prediction are following the preprocessing models, while the postprocessing models based on the error correction are rarely applied. To enhance the forecasting robustness and provide a relatively comprehensive comparison between the preprocessing and postprocessing model, this research proposes a novel hybrid model KELM-VMD-KELM by combining variational mode decomposition (VMD) and the kernel-based extreme learning machine (KELM), in which the KELM is firstly employed to forecast the daily carbon price series and obtain the initial prediction results, and then the VMD-KELM is utilized to build the predicting models for the residual error series to implement the process of error correction. The particle swarm optimization (PSO) algorithm is made a use to determine the optimal parameters of KELM and VMD. The daily average carbon price from Beijing, Guangdong and Shanghai market are selected to test the validity of the model. The results indicate that there is heterogeneity of the optimal model in different datasets. Both KELM-VMD-KELM and VMD-KELM perform well in the daily carbon price prediction. The postprocessing model can guarantee a high stability in different datasets. [ABSTRACT FROM AUTHOR]