Yang Jingling, Chen Liren, Chen Huayou
School of Big Data and Statistics, Anhui University, Hefei, 230601, China.
School of Marine Science and Technology, Tianjin University, Tianjin, 300072, China.
Sci Rep. 2025 Feb 27;15(1):7087. doi: 10.1038/s41598-025-90006-2.
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.
区间预测不仅需要准确性，还需要考虑区间宽度和覆盖率，这使得模型选择变得复杂。然而，在区间组合预测中，研究很少涉及这一挑战。为了解决这个问题，本研究引入了一种基于沙普利值的区间预测组合模型选择方法（MSIFC-SV）。该算法通过计算沙普利值来衡量每个模型的边际贡献，并根据区间得分的变化建立冗余准则。如果去除某个模型不会降低区间得分，则认为该模型是冗余的并将其排除。选择过程从所有模型开始，根据沙普利值对它们进行排序。然后根据冗余准则评估模型是否保留或去除，这个过程会一直持续，直到所有冗余模型都被排除。剩余的子集通过区间贝叶斯加权来生成区间预测组合。对碳价格的实证分析表明，在预测区间覆盖率概率（PICP）、平均预测区间宽度（MPIW）、覆盖宽度准则（CWC）和区间得分（IS）等指标上，MSIFC-SV优于单个模型和派生子集。与基准方法的比较进一步证明了MSIFC-SV的优越性。此外，MSIFC-SV还成功扩展到公共数据集——房价数据集，这表明了它的通用性。总之，MSIFC-SV提供了可靠的模型选择，并能做出高质量的区间预测。
