An integrated decomposition—Representation learning framework for multi-scale carbon price forecasting in smart energy systems

Reliable carbon price forecasts support market monitoring, policy assessment, and operational planning in smart energy systems. Yet carbon prices are volatile, non-stationary, and driven by interacting regulatory, energy, commodity, and financial conditions. This study proposes an integrated Decomposition-Representation-Integration (DRI) framework that combines complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), a lightweight decoder-only causal Transformer, and XGBoost regression. CEEMDAN separates multi-scale dynamics; causal masked self-attention jointly reconstructs cross-scale dependencies without access to future observations; and XGBoost integrates the learned representation with exogenous drivers. The framework is evaluated using a strictly causal five-fold walk-forward protocol in which preprocessing, decomposition, validation, tuning, and model fitting are confined to each training window. Its CEEMDAN-CausalTransformer-XGBoost implementation achieves a minimum MAE of 0.6583, RMSE of 0.8071, and out-of-sample 𝑅 2 of 0.7470. It consistently outperforms decomposition-only and standalone benchmarks across five tuning strategies, while Diebold-Mariano tests provide statistical evidence of improved predictive accuracy over key baselines. Prediction-path analysis suggests that gains are more visible during high-volatility periods. These results indicate that reconstructing cross-scale information improves carbon-market monitoring and provides decision support for smart energy system operators, market participants, and policymakers.