A multifactor hybrid model for carbon price interval prediction based on decomposition-integration framework

Carbon price is a pivotal element in the carbon trading sector. Accurate estimation of carbon price can offer precise guidance for the carbon market participants. This study introduces a novel prediction model encompassing both point and interval prediction for the carbon price. Firstly, to distill the volatility traits inherent in carbon price, the successive variational mode decomposition is utilized to adaptively decompose the carbon price into regular sequences. Secondly, to obtain the optimal input variables, the partial autocorrelation function and random forest are employed to filter the influencing factors and historical carbon price. Then, to avoid single model constraint, a combination model of categorical boosting and kernel extreme learning machine optimized by the sparrow search algorithm is employed for the point prediction, and the shapley additive explanation is employed to elucidate the model prediction process. Finally, to provide more efficient information, the adaptive bandwidth kernel density estimation is applied to the interval prediction. The data from Hubei carbon market is adopted as a case study, and the results indicate that the mean absolute error, mean absolute percentage error, root mean square error and R2 of the proposed model are 0.1022, 0.0022, 0.1262 and 0.9921, respectively. The historical carbon price, Brent crude oil futures settlement price and European Union allowance futures carbon price have a positive impact on carbon price, and Hushen 300 has a negative impact on carbon price. Compared with the constant kernel density estimation, the proposed model achieves higher interval coverage probability and lower interval width. Thus, the application of the hybrid model can promote the operational efficiency of the carbon market and facilitate the implementation of carbon emission reduction policies.