Point and interval forecasting of ultra-short-term carbon price in China

Accurate carbon price prediction is a reference that allows market participants to make decisions. This study adopts a total of 1,857 trading days of data from April 2, 2014, to June 15, 2022, in the Hubei carbon market, one of the first and largest pilot carbon markets in China for carbon price prediction. We propose a new framework based on the GA-VMD-CNN-BiLSTM-Attention hybrid model: a genetic algorithm (GA) is adopted to search the optimal parameter combination of variational mode decomposition (VMD); a convolutional neural network (CNN) is established to discover the relationship between influencing factors and carbon prices; a bidirectional long and short-term memory network (BiLSTM) is applied to extract time series information; and an attention mechanism is used to strengthen the influence of important information on carbon prices. Compared to 11 other models, the GA-VMD-CNN-BiLSTM-Attention model has a higher accuracy and stronger model reliability. In addition to deterministic point prediction, this study uses non-parametric kernel density estimation with the Gaussian kernel function (KDE-Gaussian) for interval forecasting. The forecasting can quantify the uncertainty of carbon prices and serve as a more practical reference for decision-makers. By revealing the particularly challenging issue that underlies carbon price forecasting, our analysis also sheds light on current low-carbon policies in China.