A transformer-based model for carbon price forecasting with self-decomposition

Abstract

Accurate carbon price forecasting is critical for the effectiveness of emissions trading, as it enables informed financial decision-making, risk management, and investment strategies while advancing global efforts to mitigate climate change. However, the inherently non-stationary and nonlinear nature of carbon prices creates substantial challenges for traditional statistical models, which often require extensive manual feature engineering when combined with machine learning. This study introduces a novel adaptive end-to-end transformer-based deep learning model that enhances both the accuracy and robustness of carbon price forecasts. The model employs a spatio-temporal attention mechanism to capture time-dependent and time-independent influences, thereby improving feature extraction. It further integrates a self-decomposition mechanism that enables adaptive preprocessing without reliance on external decomposition methods. To optimize performance, particle swarm optimization is applied for hyperparameter tuning, improving both efficiency and convergence. Empirical analyses using carbon price data from China’s Emissions Trading System (ETS) and the European Union ETS show that the proposed method consistently outperforms state-of-the-art forecasting models in both daily and multi-step prediction tasks. In daily forecasting, the model achieves mean absolute percentage errors of 3.26% for Hubei ETS, 3.71% for Guangdong ETS, 4.83% for Beijing ETS, and 1.73% for the EU ETS. These results underscore the method’s strong cross-market and cross-asset generalization, establishing it as a reliable tool for policymakers, investors, and carbon market participants.