Interval Carbon Price Prediction Based on Deep Error Correction and Bivariate Kernel Density Estimation

The core value of carbon price forecasting lies in reducing uncertainty in carbon markets and promoting the transition to a low-carbon economy. Although significant progress has been made in current carbon price forecasting models, challenges remain in the adaptability of second decomposition algorithms, the depth extraction capability of error correction algorithms, and the handling of non-normality and heteroscedasticity in carbon price data through interval algorithms. To address these issues, this paper proposes a four-stage carbon price forecasting model. First, a second decomposition is performed using ICEEMDAN-VMD optimized by the Difference Innovation Search Algorithm (DCS) and the Central Frequency Method. Next, the TCN-Transformer is used to model the decomposed components separately, with their linear summation providing the preliminary forecast. Then, an improved second decomposition algorithm (ISD) and LSTM are applied to build a deep error correction model, aiming to extract the predictable components from the preliminary forecast errors. Finally, a Bivariate Kernel Density Estimation (BKDE) is constructed using the forecast values and error values from the training set to generate interval prediction results. Case studies from Hubei and Guangzhou demonstrate that the model achieves an R² greater than 0.99 and a PICP greater than 0.95, significantly outperforming existing methods and effectively supporting the implementation of the dual-carbon strategy.