Information Leakage Prevention and Multi-Scale Feature Modeling for Carbon Emission Time Series Forecasting

Accurate carbon emission forecasting is vital for energy system optimization and carbon market decision-making. However, carbon emission data typically exhibit nonlinear and multi-scale characteristics, making them difficult to model using traditional forecasting methods. Moreover, conventional models may suffer from data leakage when future information is inadvertently used during training. To address these challenges, this study proposes an innovative forecasting framework that integrates wavelet transform (WT), rolling variational mode decomposition (RVMD), the tornado optimizer with coriolis (TOC), and the TimeXer model. In this framework, WT is first applied to filter out high-frequency noise. RVMD, combined with a sliding window mechanism, is then used to decompose the series while preventing future information leakage. The TOC algorithm adaptively optimizes RVMD parameters to enhance decomposition fidelity. Finally, the TimeXer model is employed to achieve achieves superior predictive accuracy for each mode. An empirical analysis using daily carbon emission data from China and the United States demonstrates that the proposed WT-RVMD-TOC-TimeXer framework significantly outperforms existing methods in both point and interval forecasting. The model exhibits superior accuracy, stability, and cross-regional generalization capability, achieving a favorable balance between interval coverage and compactness. Statistical tests further confirm its advantages. This study provides a systematic and practical solution for modeling complex carbon emission time series, offering both theoretical innovation and engineering applicability.