Prediction uncertainty and volatility for carbon price using an adaptive lower and upper bound estimation model

The high volatility and uncertainty of carbon price have always been two major challenges in carbon price forecasting. To solve these two challenges, an adaptive lower-and upper-bound estimation (LUBE) model with improved variational mode decomposition (VMD) and PSO-based interval optimization strategy is proposed for interval prediction of carbon price. To validate effectiveness and superiority, the adaptive LUBE model and several competitive models, including the bootstrap model, delta model, and Bayesian model, were utilized for interval prediction of carbon prices of Beijing and Shanghai. Compared with other models, the adaptive LUBE model not only has excellent coverage but also has the narrowest interval width in both training set and test set. Therefore, the excellent comparison results show that the proposed model can obtain a more reliable and higher-quality prediction interval, which can be a novel and effective carbon prices forecasting tool for governments and enterprises.