A dual decomposition integration and error correction model for carbon price prediction

Accurately predicting carbon prices is crucial for effective government decision-making and maintenance the stable operation of carbon markets. However, the instability and nonlinearity of carbon prices, driven by the complex interaction between economic, environmental, and political factors, often result in inaccurate predictions. To confront this challenge, this paper proposed a carbon price prediction model that integrates dual decomposition integration and error correction. Firstly, the variational mode decomposition optimized by the sparrow search algorithm (SVMD) is used to decompose carbon price series into intrinsic mode functions (IMFs). Secondly, a classification-prediction module is constructed to classify IMFs on complexity using fuzzy entropy. The long short-term memory networks optimized by the whale optimization algorithm (WLSTM) is employed to capture temporal dynamics and long-term dependencies within data. Conversely, lower complexity IMFs characterized by smoother trends and less erratic behavior are predicted using computationally efficient extreme learning machines (ELM). To further refine the prediction accuracy, ensemble empirical mode decomposition (EEMD) is introduced to decompose the initially predicted error series into IMFs and then predicted by classification-prediction module. Reconstruct the initial prediction IMFs and the error prediction IMFs to obtain the final prediction results. Finally, the proposed model was validated using real carbon price data from three Chinese carbon exchanges. Compared with the 15 comparison models, the performance indicators RMSE, MAE, MAPE, and R² of the proposed model have promoted at least 19.89%, 25.11%, 25.01%, and 0.79% on average. These results underscore the effectiveness and superiority in predicting carbon prices, providing a robust tool for carbon market stakeholders and climate change policymakers.