双重改进的等维递补动态GM(1,1)模型探析  

Analysis of Double Improved Dimension-fixed and Recursion-compensated Dynamic GM(1,1)Model

作　　者：汪朝阳[1,2] 苏长权[1] Wang Zhaoyang;Su Changquan(Business School,Jianghan University,Wuhan 430056,China;Wuhan City Circle Manufacturing Industry Development Research Center,Jianghan University,Wuhan 430056,China)

机构地区：[1]江汉大学商学院,武汉430056 [2]江汉大学武汉城市圈制造业发展研究中心,武汉430056

出　　处：《统计与决策》2020年第19期34-37,共4页Statistics & Decision

基　　金：武汉城市圈制造业发展研究中心主任基金项目(WZ2017J03)。

摘　　要：传统等维递补动态GM(1,1)模型存在背景值的不准确性和维数确定的随意性缺陷,文章利用牛顿插值法对背景值进行优化,采用滚动建模方法对动态递补的最优维数的选择进行改进,构建了双重改进的等维递补动态GM(1,1)模型,对湖北省GDP的发展进行了模拟。结果表明:双重优化后的等维递补动态GM(1,1)模型与传统的静态GM(1,1)模型、背景值优化的静态GM(1,1)模型以及单一优化的等维递补动态GM(1,1)模型相比,其精度分别提高了27.48%、26.93%和3.1%。可见,构建的新模型拟合精度高于传统模型,有助于相关政府部门和企业做出更为科学的经济决策。The traditional dimension-fixed and recursion-compensated dynamic GM(1,1)model has the defects of inaccuracy of background value and randomness of dimension determination.This paper uses Newton interpolation method to optimize the background value,and adopts the rolling modeling method to improve the selection of the optimal dimension of dynamic recursioncompensated.And then,the paper constructs the double-improved dimension-fixed and recursion-compensated dynamic GM(1,1)model,and simulates the development of Hubei Province’s GDP.The results show that compared with the traditional static GM(1,1)model,the static GM(1,1)model with background value optimization and the dimension-fixed recursion-compensated dynamic GM(1,1)model with single optimization,the precision of the double optimized dimension-fixed recursion-compensated dynamic GM(1,1)model is improved by 27.48%,26.93%and 3.1%,respectively.It can be seen that the fitting accuracy of the newly constructed model is higher than that of the traditional model,which helps relevant government departments and enterprises to make more scientific economic decisions.

关 键 词：灰色系统 双重改进 牛顿插值法 滚动建模 

分 类 号：F224.9[经济管理—国民经济]