Carbon price forecasting with variational mode decomposition and optimal combined model

Abstract In order to deal with non-stationary and nonlinear carbon price series, a hybrid forecasting approach is proposed in this study, which is incorporated variational mode decomposition (VMD), mode reconstruction (MR) and optimal combined forecasting model (CFM). The proposed approach introduces a new modes reconstruction method by using evolutionary clustering algorithm, and utilizes optimal combined model to forecast the reconstructed modes. The major steps of developed method can be summarized as: Firstly, carbon price is decomposed into several modes via VMD model, and the modes are obtained adaptively. Secondly, the comprehensive contribution index (CCI) of each mode is calculated and modes are further reconstructed by evolutionary clustering algorithm according to CCI. Then, a new sub-series called virtual modes (V-Modes) is defined and obtained. Thirdly, the optimal combined forecasting model is developed to forecast the V-Modes. In the end, the final forecasting results are obtained by summing the forecasts of V-Modes. For illustration and comparison, the carbon price data from Shenzhen and Hubei Province in China are shown as numerical examples. The empirical results confirm that the proposed approach outperforms benchmark models in terms of some statistical measures and robustness. Therefore, the proposed hybrid approach can be utilized as an effective model for the forecasting of carbon price.