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优化的GM(1,1)模型及其适用范围
引用本文:刘斌,赵亮,翟振杰,党耀国,张荣.优化的GM(1,1)模型及其适用范围[J].南京航空航天大学学报,2003,35(4):451-454.
作者姓名:刘斌  赵亮  翟振杰  党耀国  张荣
作者单位:1. 南京航空航天大学经济与管理学院,南京,210016;河南农业大学计算机科学系,郑州,450002
2. 郑州百福期货有限公司,郑州,450008
3. 南京航空航天大学经济与管理学院,南京,210016
4. 河南农业大学计算机科学系,郑州,450002
基金项目:国家博士点基金 (2 0 0 2 0 2 870 0 1 ),河南省自然科学基金 (9940 1 1 80 )资助项目
摘    要:在已有灰色理论的基础上,利用“最小二乘法”确定GM(1,1)白化权函数的时间响应函数中的常数c,摈弃了传统GM(1,1)把原始序列中x^(0)(1)作为初始条件的欠科学的做法,构建了时间响应函数的优化模型。经大量的数据模拟和预测,发现优化的GM(1,1)模型各项指标均优于传统的GM(1,1)模型,且拓宽了其适用范围。

关 键 词:GM(1,1)模型  适用范围  模型优化  时间响应函数  最小二乘法  灰色系统理论
文章编号:1005-2615(2003)04-0451-04
修稿时间:2002年11月14

Optimum Model of GM(1,1) and Its Suitable Range
LIU Bin ,ZHAO Liang ,ZHAI Zhen-jie ,DANG Yao-guo ,ZHANG Rong.Optimum Model of GM(1,1) and Its Suitable Range[J].Journal of Nanjing University of Aeronautics & Astronautics,2003,35(4):451-454.
Authors:LIU Bin    ZHAO Liang  ZHAI Zhen-jie    DANG Yao-guo  ZHANG Rong
Institution:LIU Bin 1,2,ZHAO Liang 3,ZHAI Zhen-jie 1,2,DANG Yao-guo 1,ZHANG Rong 2
Abstract:GM(1,1), as a kind of forecasting model applied widely, is the most important content or the core of grey system theory. Based on the theories, this paper utilizes the method of "the least square estimate" to discover the constant number c in the time response sequence of Whiterization equation of GM (1,1) after finding the development coefficient and grey action quantity, and abandons the modus operandi to regard x (0)(1), the first number of raw sequence is used as the initial value of the Whiterization equation of GM(1,1) because we think it be unscientific. Then, the optimum time response sequence of Whiterization equation of GM(1,1) is established. By contrasting the optimum one to the GM(1,1) about the simulation and prediction, we can conclude that the optimum one is superior in prediction and simulation, and it is interesting that the optimum one widen its suitable range.
Keywords:GM(1  1) model  time response sequence  least square method  forecast
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