多频率信息协同下的季节性混频灰色预测模型及其应用  

Seasonal mixing grey prediction model and its application under collaboration of multiple frequency information

作　　者：苟小义 米传民[1,2] 曾波 王俊杰[1] GOU Xiao-yi;MI Chuan-min;ZENG Bo;WANG Jun-jie(College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China;Key Laboratory of Intelligent Decision and Digital Operations,Ministry of Industrial and Information Technology,Nanjing 210016,China;College of Management Science and Engineering,Chongqing Technology and Business University,Chongqing 400067,China)

机构地区：[1]南京航空航天大学经济与管理学院,南京210016 [2]智能决策与数字化运营工业和信息化部重点实验室,南京210016 [3]重庆工商大学管理科学与工程学院,重庆400067

出　　处：《控制与决策》2025年第4期1163-1171,共9页Control and Decision

基　　金：国家自然科学基金项目(72071023,72001107,72271120);江苏省研究生科研与实践创新计划项目(KYCX24_0521)。

摘　　要：针对协同利用多频率信息进行建模时存在变量频率不齐,以及高频变量通常具有季节性影响的问题,构建季节性混频灰色预测模型(SMFGM(1,N)).首先,所提出新模型通过引入Nakagami函数来实现变量间频率对齐,基于季节因子消除变量的季节性影响,添加非线性项来反映系统受时间因素的非线性影响;然后,为了辨识新模型中的滞后参数,将Nakagami函数与经典灰色关联度模型相结合,提出混频灰色关联度模型,以识别不同频率变量间的关联关系;最后,基于年度GDP和季度税收收入案例,将所提出新模型与混频数据抽样模型、其他灰色预测模型、神经网络模型以及统计模型进行对比分析.分析结果表明:SMFGM(1,N)模型具有更优异的建模性能,能够有效处理具有季节性规律的混频数据预测问题,为多频率信息系统建模提供了新的方法.When modeling with the collaborative use of multi-frequency information,the issues of inconsistent variable frequencies and the seasonal effects often associate with high-frequency variables arise.Therefore,this paper proposes a seasonal mixed-frequency grey prediction model(SMFGM(1,N)).The model aligns variable frequencies by introducing the Nakagami function,eliminates the seasonal effects of variables based on seasonal factors,and incorporates nonlinear terms to capture the nonlinear impacts of time on the system.Additionally,to identify the lag parameters in the model,the Nakagami function is combined with the classical grey relational model to propose a mixed-frequency grey relational model,which helps identify the relationships between variables with different frequencies.Finally,using a case study of annual GDP and quarterly tax revenue,the model is compared with the mixed-frequency data sampling model,other grey prediction models,neural network models,and statistical models.The results demonstrate that the SMFGM(1,N)model has superior modeling performance and effectively addresses the prediction problems of mixed-frequency data with seasonal patterns,providing a new method for modeling multifrequency information systems.

关 键 词：SMFGM(1 N)模型 混频灰色关联度模型 Nakagami函数 季节性因素 多频率信息 税收收入预测 

分 类 号：N941.5[自然科学总论—系统科学]