Intelligent carbon price prediction system based on improved secondary decomposition and multi-head attention bidirectional long short-term memory (BiLSTM) model.

Carbon price forecasting (CPF) plays a critical role in maintaining the stability of carbon financial markets and promoting global cooperation on emission reduction. However, carbon price series often exhibit significant volatility and nonlinearity, making high-precision forecasting extremely challenging. In particular, after decomposing the original sequence, effectively eliminating pseudo-information interference and accurately extracting potential features remain key difficulties. To address these issues, this paper proposes a hybrid forecasting model based on improved secondary decomposition (ISD) and a bidirectional long short-term memory network integrated with a Multi-Head attention mechanism (MAM-BiLSTM). In the decomposition stage, two decomposition methods are combined with an adaptive frequency and energy threshold method (AFETM) to improve the precision of high-frequency information extraction. In the prediction stage, the MAM optimizes the temporal feature weighting of BiLSTM, thereby enhancing the model’s ability to capture complex temporal patterns. Meanwhile, the grey wolf optimizer (GWO) is employed to adaptively tune the key parameters of both variational mode decomposition (VMD) and BiLSTM, further improving the model’s generalization performance. Empirical results based on three representative carbon market datasets demonstrate that the proposed model outperforms eleven baseline models. For example, in terms of mean absolute percentage error (MAPE), the forecasting accuracy is improved by 1.314%, 3.630%, and 7.818% compared with the best-performing baselines. These results confirm the effectiveness and robustness of the proposed model and provide strong support for carbon market risk assessment and policy-making.