Hybrid intelligent framework for carbon price prediction using improved variational mode decomposition and optimal extreme learning machine

As the climate problem continues to worsen, carbon trading markets for energy conservation and emission reduction have been established in many countries. Accurate forecasting of carbon trading prices is not only a realistic problem, but also brings huge challenges to relevant researches. In this study, a novel predicting model is proposed to predict carbon price. And this model combines the advantages of the improved variational mode decomposition (IVMD) algorithm, multiscale entropy (MSE) algorithm, and the extreme learning machine (ELM) model improved by the intelligent optimization algorithm. Firstly, center frequency (CF) and mutual information (MI) entropy are utilized to jointly determine the number of decomposition layers of the variational mode decomposition (VMD), and avoid the problem of excessive decomposition. Subsequently, the complexity of each intrinsic mode function (IMF) from the improved variational mode decomposition is calculated by multiscale entropy, and intrinsic mode functions are recombined to reduce the complexity of subsequent modeling. At the last, the extreme learning machine optimized by the sparrow search algorithm (SSA) is adopted to model and predict the different sequence combinations. The performance indicators of the proposed model are significantly lower than others. For example, the root mean square error (RMSE) of the proposed model is 0.6653 in Hubei market, 0.9719 in Guangdong market and 1.2819 in Shanghai market. Additionally, the optimized extreme learning machine model is more suitable for the prediction of time series, which also provides an effective forecasting tool for related researchers. (C) 2021 Elsevier Ltd. All rights reserved.