Shapley value-driven superior subset selection algorithm for carbon price interval forecast combination

Interval prediction requires not only accuracy but also the consideration of interval width and coverage, making model selection complex. However, research rarely addresses this challenge in interval combination forecasting. To address this issue, this study introduces a model selection for interval forecast combination based on the Shapley value (MSIFC-SV). This algorithm calculates Shapley values to measure each model's marginal contribution and establishes a redundancy criterion on the basis of changes in interval scores. If the removal of a model does not decrease the interval score, it is considered redundant and excluded. The selection process starts with all the models and ranks them by their Shapley values. Models are then assessed for retention or removal according to the redundancy criterion, which continues until all redundant models are excluded. The remaining subset is used to generate interval forecast combinations through interval Bayesian weighting. Empirical analysis of carbon price shows that MSIFC-SV outperforms individual models and derived subsets across metrics such as prediction interval coverage probability (PICP), mean prediction interval width (MPIW), coverage width criterion (CWC), and interval score (IS). Comparisons with benchmark methods further demonstrate the superiority of MSIFC-SV. Furthermore, MSIFC-SV is also successfully extended to the public dataset-housing price dataset, this indicates its universality. In summary, MSIFC-SV provides reliable model selection and delivers high-quality interval forecasts.