Hybrid carbon price forecasting using a deep augmented FEDformer model and multimodel optimization piecewise error correction

Accurate and robust carbon price forecasting is crucial for stabilizing the carbon financial market and reducing reliance on fossil resources. This study introduces a novel hybrid model, combining a deep augmented frequency enhanced decomposed transformer (DA-FEDformer), improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), and a multimodel optimization piecewise error correction, for accurate carbon price prediction. To leverage frequency domain information, the proposed DA-FEDformer model enhances the decoder and encoder layers by incorporating a multilayer perceptron layer. A novel improved kernel mean square error loss function is devised for the model, and the evolved sign momentum optimizer is employed for further optimization. To further improve the prediction accuracy, a data postprocessing method is integrated into the model. The DA-FEDformer predicts the carbon price, and the ICEEMDAN method decomposes the error sequence into subsequences. These subsequences are forecasted using five different models. Finally, the DA-FEDformer prediction results and the error correction results are combined to obtain the final carbon price sequence. This hybrid model is systematically evaluated using carbon price data from Hubei, Guangzhou, and Beijing in China. The results demonstrate that the hybrid model achieves favorable performance on three datasets. This innovative approach provides a promising solution for carbon price forecasting in China.