Forecasting carbon price using a hybrid framework based on Bayesian optimization algorithm

With the European Union (EU) introducing the Carbon Border Adjustment Mechanism (CBAM), accurately forecasting EU carbon price is crucial for exporters to estimate export costs, plan low-carbon strategies, and mitigate trade risks. In the petroleum sector, carbon pricing directly influences upstream investment returns and carbon intensity targets, thereby closely linking emissions markets with fossil energy strategies. Existing models often fail to fully capture the nonlinear, non-stationary nature of carbon prices and their dependence on external factors. This study proposes a novel hybrid framework that combines improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) with gated recurrent unit-convolutional neural network-long short-term memory network-Bayesian optimization (GRU-CNN-LSTM-BO). Empirical results based on the EU emissions trading system (ETS) market demonstrate that the proposed model significantly improves forecasting accuracy. Among all experiments, the proposed GRU-CNN-LSTM-BO framework achieves the best performance, yielding the lowest MAE (1.3872), RMSE (1.7038), MAPE (0.0166), and MSPE (0.0004), as well as the highest R² (0.9400). Compared to all benchmark models, the GRU-CNN-LSTM-BO model achieves reductions in MAE and RMSE ranging from 5.38% to 63.65% and 8.97% to 64.41%, respectively. To further validate the generalization ability and predictive performance of the proposed model, it is also applied to China's ETS. The results show that the GRU-CNN-LSTM-BO model also performs very well in China's ETS.