A novel carbon price forecasting model integrating mixed-frequency modeling into the transformer architecture from a multi-factor perspective

Previous carbon price forecasting studies are mostly limited to the same-frequency prediction, and the predictive validity of the modeling approach using mixed-frequency data has been neglected. Therefore, to fill this research gap and enhance the accuracy of carbon price prediction, this study proposes a novel hybrid forecasting model by integrating multiple external factors, deep learning, and mixed-frequency modeling. Firstly, this study introduces twenty-two variables from four categories of influencing factors, including energy commodities, market indicators, economic indicators, and environmental indicators, and the feature selection method reduces data dimensionality to obtain the input factors. Subsequently, this study innovatively incorporates the mixed-frequency data sampling regression (MIDAS) into the Transformer architecture, and constructs the hybrid forecasting model, i.e., the multi-factor Transformer-MIDAS model, which realizes the mixed-frequency prediction of the low-frequency carbon price by using the high-frequency input factors. Furthermore, relevant experiments are designed and the results show that the proposed hybrid model can robustly predict the two carbon price datasets for Guangdong and Shanghai with mean absolute errors of 1.14 and 0.86, while the mean absolute percentage errors are 1.52 % and 1.40 %, respectively, which significantly outperforming the benchmark model. These experimental results confirm the practicality of the proposed hybrid model, and verify that the mixed-frequency modeling approach can efficiently exploit the rich predictive information in the mixed-frequency data to achieve timely prediction.