Causal carbon price interval prediction using lower upper bound estimation combined with asymmetric multi-objective evolutionary algorithm and long short-term memory

Recently the interval forecasting of carbon price is investigated by advanced research since it can better quantify the uncertainty and reliability of the forecast value in comparison with point forecasting. However, this kind of model is always limited to the distribution-based method, which can only conduct symmetric prediction intervals and heavily rely on accurate point prediction and preprogrammed errors' probability distribution. Therefore, we make the following improvements for enriching research on the interval prediction of carbon price and providing more references for researchers in related fields. Firstly, lower upper bound estimation model (LUBE) is employed to conduct the prediction interval rather than the distribution-based method, and this designer can generate asymmetric upper and lower bounds without the need for assumptions and humanly devised parameters. Secondly, the causal inference is applied to the feature selection rather than the correlation analysis, which can well improve the generalization ability of prediction model. Thirdly, we improved the objectives when using multi-objective evolutionary algorithms for searching more efficient solutions in less time. Finally, through various experiments the most effective combination of LUBE and the ensemble method are verified, which are also proved by experiments.