Forecasting Carbon Price with Secondary Decomposition Algorithm and Optimized Extreme Learning Machine

Abstract

Carbon trading is a significant mechanism created to control carbon emissions, and the increasing enthusiasm for participation in the carbon trading market has forced the emergence of higher-precision carbon price prediction models. Facing the complexity of carbon price time series, this paper proposes a carbon price forecasting hybrid model based on secondary decomposition and an improved extreme learning machine (ELM). First, the complementary ensemble empirical mode decomposition with adaptive noise (CEEMDAN) is utilized to decompose the carbon price several intrinsic modal functions to initially weaken the non-linearity of the original carbon price data. Secondly, the first intrinsic mode function (IMF1) with the strongest volatility is processed by the variational mode decomposition (VMD). Then, the partial autocorrelation function (PACF) is applied to obtain the model input variables for subsequences. Finally, the ELM improved by the bald eagle search (BES) algorithm is utilized to make predictions. In the empirical analysis, five actual datasets from three carbon markets are used to verify the prediction performance of the proposed model. Based on the six evaluation indicators of the predicted results, the proposed model is the best performer among all models, which suggests that CEEMDAN-VMD-BES-ELM is effective and stable in predicting carbon price.