摘要
针对传统的MGM(1,m)模型存在模拟精度和预测精度不高的问题,文章给出了改进的初值和背景值优化的MGM(1,m)模型。在模型初值的选取上,选取使得模拟值的平均相对误差达到最小的向量X(1)(i)作为初值;在模型背景值的构造上,提出结合辛普森3/8公式的动态序列模型来求解背景值的方法。最后以两组指数型数据序列为例建立了传统MGM(1,2)模型及改进后的模型,并进行数据模拟和预测。结果表明,改进后的MGM(1,m)模型的模拟精度和预测精度均有显著地提高,从而验证了模型的有效性和可行性。
Aiming at the problem that the traditional MGM(1,m)model has low accuracy in simulation and prediction,this paper proposes an improved MGM(1,m)model of optimizing initial and background value.In selecting model initial value,the paper takes as the initial value the vector[X(1)(I)]that minimizes the average relative error of the simulation value.For the construction of the model background value,the paper proposes a method to solve the background value by combining the dynamic sequence model of Simpson 3/8 formula.Finally,the paper takes two sets of exponential data series as examples to establish the traditional MGM(1,2)model and the improved model,and also carries out data simulation and prediction.The results show that the simulation accuracy and prediction accuracy of the improved MGM(1,m)model are significantly boosted,which verifies the validity and feasibility of the proposed model.
作者
张红敏
沙秀艳
王玉凤
李慧诚
Zhang Hongmin;Sha Xiuyan;Wang Yufeng;Li Huicheng(School of Statistics,Qufu Normal University,Qufu Shandong 273165,China;School of Mathematical Sciences,Qufu Normal University,Qufu Shandong 273165,China)
出处
《统计与决策》
CSSCI
北大核心
2020年第1期15-19,共5页
Statistics & Decision
基金
国家自然科学基金资助项目(11171179
11571198
11371183)
全国统计科学研究项目(2019LY47)
国家级大学生创新创业训练计划项目(201810446103)
