Multi-step-ahead and interval carbon price forecasting using transformer-based hybrid model

Forecasting China carbon price using an error-corrected secondary decomposition hybrid model integrated fuzzy dispersion entropy and deep learning paradigm

Forecasting China's carbon price accurately can encourage investors and manufacturing industries to take quantitative investments and emission reduction decisions effectively. The inspiration for this paper is developing an error-corrected carbon price forecasting model integrated fuzzy dispersion entropy and deep learning paradigm, named ICEEMDAN-FDE-VMD-PSO-LSTM-EC. Initially, the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) is used to primary decompose the original carbon price. Subsequently, the fuzzy dispersion entropy (FDE) is conducted to identify the high-complexity signals. Thirdly, the variational mode decomposition (VMD) and deep learning paradigm of particle swarm optimized long short-term memory (PSO-LSTM) models are employed to secondary decompose the high-complexity signals and perform out-of-sample forecasting. Finally, the error-corrected (EC) method is conducted to re-modify and strengthen the above-predicted accuracy. The results conclude that the forecasting performance of ICEEMDAN-type secondary decomposition models is significantly better than the primary decomposition models, the deep learning PSO-LSTM-type models have superiority in forecasting China carbon price, and the EC method for improving the forecasting accuracy has been proved. Noteworthy, the proposed model presents the best forecasting accuracy, with the forecasting errors RMSE, MAE, MAPE, and Pearson's correlation are 0.0877, 0.0407, 0.0009, and 0.9998, respectively. Especially, the long-term forecasting ability for 750 consecutive trading prices is outstanding. Those conclusions contribute to judging the carbon price characteristics and formulating market regulations.