An integrated prediction framework combining variational mode optimization decomposition, empirical quantile regression, and QLattice for dynamic point and interval prediction of carbon prices

Accurate carbon price prediction is crucial for the stability and development of carbon trading markets. To improve the accuracy and reliability of prediction results, this study proposes an integrated prediction framework that combines point prediction and interval prediction: TGSINFO-VMD-NEQQLattice. The framework introduces a vector-weighted mean optimization algorithm (TGSINFO) improved based on Tent chaotic mapping and Golden Sine Algorithm (Gold-SA), which uses the minimum permutation entropy (MinPE) of subsequences as the optimization objective to optimize the hyperparameters of Variational Mode Decomposition (VMD), thereby enabling VMD to decompose the carbon price series more precisely. Additionally, to fill the research gap regarding the interpretability of carbon price prediction results, this framework applies the QLattice model to carbon price prediction for the first time. The QLattice model not only demonstrates superior prediction performance but also provides a mathematical expression of the prediction results, significantly enhancing interpretability. In the final interval prediction stage, the framework combines the QLattice point prediction results with a Non-parametric prediction interval construction method based on empirical quantile regression (NEQ) to achieve interval prediction. Empirical tests across multiple carbon markets in China show that the proposed framework surpasses others, offering robust decision-making support. The source code for TGSINFO-VMD-NEQQLattice is publicly available at: https://github.com/StriveOrange/TGSINFO-VMD-NEQQLattice.git.