Carbon Allowance Price Forecasting Based on a Multi-Scale Decomposition Strategy and a TCN–LSTM Hybrid Model: A Case Study of Hubei Province

The carbon allowance price series exhibits nonlinearity, non-stationarity, and high noise due to multiple factors. Accurate forecasting is crucial to the stability of the carbon market and to resource allocation. This paper proposes a forecasting framework using multi-scale decomposition and a TCN–LSTM hybrid model. First, the original carbon allowance price series is decomposed using CEEMDAN optimized by PSO. Then, VMD performs secondary decomposition of complex components based on sample entropy. Next, transfer entropy identifies causal relationships between each component and the original series, enabling reconstruction based on causality. Finally, a TCN–LSTM model uses reconstructed sequences to forecast carbon prices. The method achieves high-precision short-term forecasts using only the carbon allowance price series, avoiding reliance on external variables. Empirical results on the Hubei carbon market show an optimal lag of 3, with R2 = 0.8873, outperforming the single LSTM and TCN models and achieving a lower RMSE. The forecast using January–March 2026 data shows stable carbon prices with slight fluctuations. This study provides a reliable method for data-constrained short-term carbon price forecasting, supporting decision-making and policy assessment.