Carbon Price Forecasting Using Optimized Sliding Window Empirical Wavelet Transform and Gated Recurrent Unit Network to Mitigate Data Leakage

Precise forecasts of carbon prices are crucial for reducing greenhouse gas emissions and promoting sustainable, low-carbon development. To mitigate noise interference in carbon price data, hybrid models integrating data decomposition techniques are commonly utilized. However, it has been observed that the improper utilization of data decomposition techniques can lead to data leakage, thereby invalidating the model’s practical applicability. This study introduces a leakage-free hybrid model for carbon price forecasting based on the sliding window empirical wavelet transform (SWEWT) algorithm and the gated recurrent unit (GRU) network. First, the carbon price data are sampled using a sliding window approach and then decomposed into more stable and regular subcomponents through the EWT algorithm. By exclusively employing the data from the end of the window as input, the proposed method can effectively mitigate the risk of data leakage. Subsequently, the input data are passed into a multi-layer GRU model to extract patterns and features from the carbon price data. Finally, the optimized hybrid model is obtained by iteratively optimizing the hyperparameters of the model using the tree-structured Parzen estimator (TPE) algorithm, and the final prediction results are generated by the model. When used to forecast the closing price of the Guangdong Carbon Emission Allowance (GDEA) for the last nine years, the proposed hybrid model achieves outstanding performance with an R 2 value of 0.969, significantly outperforming other structural variants. Furthermore, comparative experiments from various perspectives have validated the model’s structural rationality, practical applicability, and generalization capability, confirming that the proposed framework is a reliable choice for carbon price forecasting.