基于组合插值的GM(1,1)模型背景值的改进  

Optimization of background value in GM(1,1) model based on combination interpolation

作　　者：李凯 张涛[1,2] Li Kai;Zhang Tao(School of Information Management&Engineering,Shanghai University of Finance&Economics,Shanghai 200433,China;Shanghai Key Laboratory of Financial Information Technology,Shanghai University of Finance&Economics,Shanghai 200433,China)

机构地区：[1]上海财经大学,信息管理与工程学院,上海200433 [2]上海财经大学,上海市金融信息技术研究重点实验室,上海200433

出　　处：《计算机应用研究》2018年第10期2994-2999,共6页Application Research of Computers

基　　金：国家自然科学基金资助项目(71171126);上海市科学技术委员会“科技创新行动计划”资助项目(16511104704,17DZ1100504);国家教育部高等学校博士学科点专项科研基金资助项目(20130078110001);上海财经大学2017年研究生创新基金资助项目(CXJJ-2017-423)

摘　　要：针对GM(1,1)模型预测误差偏大的问题,对GM(1,1)模型背景值的构造形式进行了研究。为了能够更加有效地降低GM(1,1)模型的预测误差,提出了基于辛普森3/8公式和牛顿插值公式的组合插值方法来构造出新的GM(1,1)模型的背景值。在GM(1,1)模型的建模过程中,由于原始建模数据序列中的第一个数据没有参与建模,导致原始数据序列的数据资源利用效率降低,影响了GM(1,1)模型预测精度。所以,可以通过把灰色协调系数b加在原始建模数据序列前面的方法,使第一个数据能够参与到GM(1,1)模型的建模过程中。为了检验模型的改进效果,进行了原始建模数据类型分别为纯指数型数据序列、稳定型数据序列和缺失型数据序列的三组实验。对每组测试实验的预测结果进行对比分析可以发现,基于组合插值方法对GM(1,1)模型的背景值进行改进,可以极大地降低GM(1,1)模型的模拟和预测误差。改进后的模型具有比较好的预测稳定性,增强了GM(1,1)模型的适用性。Aiming at solving the problem of large prediction error in GM(1,1),model,this paper explored the construction of background value for GM(1,1)model.In order to reduce the prediction error of GM(1,1)model,it proposed a new interpolation method based on Simpson’s 3/8 formula and Newton interpolation formula to construct the background value of the improved GM(1,1)model.Since the first data of GM(1,1)model was not involved in modeling,the data resource utilization efficiency of the original data sequence was reduced,adversely affecting the prediction accuracy of GM(1,1)model.Therefore,the gray coordination coefficient b could be put in front of the original modeling data sequence so that the first data of GM(1,1)model could be utilized during modeling.In order to verify the performance of the improved GM(1,1)model,it carried out three sets of experiments,in which the original modeling data types were pure exponential data sequences,stable data sequences and missing data sequences respectively.And by comparing and analyzing the prediction results of each set of experiments,it is found that the improved GM(1,1)model can dramatically decrease the simulation error and prediction error of GM(1,1)model.The improved GM(1,1)model is stable in prediction,thus extending the application of GM(1,1)model.

关 键 词：GM(1 1)模型 改进的GM(1 1)模型 初始值 背景值 组合插值 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]