CEEMDAN–FADE: A Data-Driven Frequency-Adaptive Ensemble Framework for Carbon-Price Forecasting

Accurate and reliable carbon-price forecasts can provide scientific support for allowance trading, corporate risk management, and emission-reduction policymaking. However, carbon prices exhibit pronounced nonlinearity, nonstationarity, and multiscale dynamics, and existing studies mainly employ a single model uniformly for all decomposed components, with obvious limitations in matching model capability to component complexity and in adapting combination weights to changing market conditions. To fill these gaps, this study constructs CEEMDAN–FADE, a frequency-adaptive ensemble framework integrating signal decomposition, complexity-based reconstruction, data-driven model selection, and dynamic weighting. Specifically, CEEMDAN decomposition is followed by sample entropy-based K-means reconstruction, thus separating market noise from trend-driven movements. Subsequently, exogenous factors are screened for each reconstructed component, and the selected factors are used to configure component-specific inputs. Then, top-performing models are selected for each component from a heterogeneous pool of statistical, machine-learning, and deep-learning approaches according to validation performance, and combined through rolling dynamic weights estimated with Huber loss. Finally, empirical results in China’s Hubei and Guangdong carbon markets show that the proposed system significantly outperforms 17 benchmark models, reducing RMSE by 18.70% and 46.24% relative to the strongest benchmark, with Diebold–Mariano tests confirming significance. A forecast-based trading analysis further reveals improved profitability and risk-adjusted performance, indicating good robustness and practical applicability.