离散型灰色预测模型的无偏性与自适应性及其应用  

Unbiased and Adaptive of Discrete Grey Prediction Model and Its Application

作　　者：李树良[1] 杨爽艺 曾波[1] 孟伟[1] 白云[1] Li Shuliang;Yang Shuangyi;Zeng Bo;Meng Wei;Bai Yun(School of Management Science and Engineering,Chongqing Technology and Business University,Chongqing 400067,China)

机构地区：[1]重庆工商大学管理科学与工程学院,重庆400067

出　　处：《中国管理科学》2024年第8期149-158,共10页Chinese Journal of Management Science

基　　金：国家自然科学基金项目(72071023);重庆市自然科学基金项目(CSTB2023NSCQ-MSX0365,CSTB2023NSCQ-MSX0380);重庆市教委科学技术研究重大项目(KJZD-M202300801);重庆市研究生导师团队建设项目(yds223006);重庆工商大学重点科研平台(企业管理研究中心)开放课题(KFJJ2022053);重庆市社科规划重点项目(2022NDZD10)。

摘　　要：无偏性与自适应性是灰色预测模型的两个重要性质,是研究模型结构及性能的基础。首先,文章以矩阵为工具,从理论上严格证明了两类常见离散灰色预测模型的无偏性。结果表明:双参数离散灰色预测模型DGM(1,1)仅对齐次指数序列具有无偏性,而三参数离散灰色预测模型TDGM(1,1)则对齐次指数/非齐次指数/线性函数序列均具有无偏性。然后,从模型结构角度对TDGM(1,1)模型面向不同特征序列的自适应性进行了分析,验证了模型结构自适应性与无偏性之间的内在联系。最后,应用TDGM(1,1)模型对世界新能源汽车销售量进行建模,并对预测结果进行了比较和分析。本研究对丰富和完善灰色预测理论具有积极意义。Unbiasedness and self-adaptability are two important properties of grey prediction model and the basis of studying the structure and performance of the model.The existing studies have mostly verified unbiased from the perspective of examples,without strict mathematical proof,and less analysis of the relationship between unbiased and adaptive.Firstly,using matrix theory,the unbiasedness of two kinds of common discrete grey prediction models is strictly proved in theory and verified by homogeneous index/nonhomogeneous index/linear function sequence.The results show that the two parameter discrete grey prediction model DGM(1,1)is unbiased only for the homogeneous exponential sequence,while the three parameter discrete grey prediction model TDGM(1,1)is unbiased for the exponential/non-homogeneous exponential/linear function sequence.Then,the adaptability of TDGM(1,1)to different feature sequences is analyzed from the perspective of model structure,and the internal relationship between self-adaptability and unbiased of model structure is verified.Finally,the TDGM(1,1)model is applied to forecast the world sales of new energy vehicles,and the prediction results are compared and analyzed.This study has positive significance for enriching and perfecting the grey prediction theory.

关 键 词：离散型灰色预测模型 模型无偏性 模型自适应性 世界新能源汽车销量预测 

分 类 号：N941.5[自然科学总论—系统科学]