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中国管理科学 ›› 2025, Vol. 33 ›› Issue (7): 178-186.doi: 10.16381/j.cnki.issn1003-207x.2022.2444

• • 上一篇    

纵横维度视角下的新型季节离散灰色预测模型及其应用

苟小义1, 米传民1(), 曾波2, 李明珠1, 徐盈婷3   

  1. 1.南京航空航天大学经济与管理学院,江苏 南京 210016
    2.重庆工商大学管理科学与工程学院,重庆 400067
    3.无锡太湖学院艺术学院,江苏 无锡 214000
  • 收稿日期:2022-11-09 修回日期:2023-02-15 出版日期:2025-07-25 发布日期:2025-08-06
  • 通讯作者: 米传民 E-mail:cmmi@nuaa.edu.cn
  • 基金资助:
    国家自然科学基金项目(72071023);江苏省研究生科研与实践创新计划项目(KYCX24_0521)

A Novel Seasonal Discrete Grey Forecasting Model based on Transverse and Longitudinal Dimensions and Its Application

Xiaoyi Gou1, Chuanmin Mi1(), Bo Zeng2, Mingzhu Li1, Yingting Xu3   

  1. 1.College of Economics & Management,Nanjing University of Aeronautics & Astronautics,Nanjing 210016,China
    2.School of Management Science and Engineering,Chongqing Technology and Business University,Chongqing 400067,China
    3.School of Atr,Wuxi Taihu College,Wuxi 214000,China
  • Received:2022-11-09 Revised:2023-02-15 Online:2025-07-25 Published:2025-08-06
  • Contact: Chuanmin Mi E-mail:cmmi@nuaa.edu.cn

摘要:

季节数据具有季节波动性、周期连贯性、阶段差异性等多重复杂特征,这为其预测模型的科学构建带来了挑战。为此,本文首先基于时序数据矩阵化处理方法,实现了纵横维度双重视角的季节波动性特征考虑;其次,通过虚拟变量的引入及累加阶数的差异化设计,构建了新型实域分数阶离散灰色预测模型,实现了季节数据周期连贯性与阶段差异性等特征的有效模拟;然后,利用粒子群算法对新模型各变量阶数在实域范围内进行同步优化,以进一步提高新模型建模性能,通过两篇文献案例建模显示,新模型误差较对比文献模型分别下降约77%与82%。最后,将新模型用于解决我国GDP季度数据的预测问题,结果显示,新模型误差为0.813%,其他同类模型误差分别为2.545%、1.517%与2.667%。本研究成果为研究季节数据的预测问题提供了一种新的建模手段,对完善和丰富灰色预测模型方法体系具有积极意义。

关键词: 季节离散灰色预测模型, 实域差异化分数阶, 纵横维度双重视角, 季度GDP预测

Abstract:

Seasonal data have multiple complex characteristics such as seasonal fluctuation, cycle coherence, and stage variability, which bring challenges to the scientific construction of its forecasting models. To this end, firstly based on the matrixed processing method of time-series data, the dual perspectives of transverse and longitudinal dimensions of seasonal volatility characteristics are considered. Then, a new real domain fractional discrete grey prediction model is constructed through the introduction of dummy variables and the differential design of accumulation orders, realizing the effective simulation of the characteristics of seasonal data cycle coherence and stage variability. And a particle swarm algorithm is used to synchronize and optimize each variable of the new model in the real domain to further improve the modeling performance of the new model. Also, the modeling by two literature cases shows that the new model error decreases by about 77% and 82%, respectively, compared with the comparative literature models. Finally, the new model is applied to solve the forecasting problem of China's quarterly GDP data, and the results show that the error of the new model is 0.813%, while others are 2.545%, 1.517% and 2.667%, respectively. The research results provide a new modeling tool for studying the forecasting problem of seasonal data, which is of positive significance for improving and enriching the grey forecasting model method system.

Key words: seasonal discrete grey forecasting model, real domain differentiation fractional order, dual perspective of transverse and longitudinal dimensions, quarterly GDP forecasting

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