An optimal multi-scale ensemble transformer for carbon emission allowance price prediction based on time series patching and two-stage stabilization

Accurate carbon price forecasting is crucial for carbon dioxide emission reduction and low-carbon transition of social development. This study proposes an optimal multi-scale ensemble transformer for carbon price prediction, leveraging time series patching and two-stage stabilization. Firstly, an adaptive feature extraction and entropy recombination method is constructed, which can effectively mine the latent features in the sequence. Through modal fusion, information of different scales can be fully integrated to perceive the dynamic change of carbon price. Then, an enhanced Transformer prediction model is constructed by the time series patching and two-stage stabilization, which can capture local temporal information and long-term dependencies more effectively. Finally, considering the different contributions of different subsequences, an intelligent weighted integration algorithm is designed to determine the optimal weight for each sequence. Empirical tests of four Chinese carbon markets show that the mean absolute percentage error (MAPE) of the forecast results is in the range of 0.93 %–2.18 % surpassing all control models. The results demonstrate the model's accuracy and robustness, providing a reliable tool for carbon price formulation, optimizing resource allocation, and supporting the healthy development of carbon markets.