针对单调增长原始数据序列, 文章在理论上讨论白化型与内涵型GM(1,1)(grey forecasting model)模型解之间的相对误差. 在推导出两个模型解之间的相对误差上界表达式的基础上, 作者研究了相对误差上界函数的性质, 讨论了相对误差一致上界关于原始数据序列长度n的单调性. 结果表明当发展系数位于[-1/(n+1),0]内时, 白化型与内涵型GM(1,1)模型解之间的相对误差上界是0.9%,可以合理使用白化模型代替内涵模型; 而发展系数在区间[-2/(n+1),0]内时, 这两个模型解之间的相对误差可能达到8.64%, 此时白化模型代替内涵模型须较谨慎地使用.
Abstract
This paper discusses theoretically the relative error between the solutions of whitenization grey forecasting model (GM(1,1) model) and connotation GM(1,1) model with a monotone increasing raw sequence. The expressions of relative error upper bound between the solutions of these two models are derived first. Then the authors study the properties of the error upper bound function. The investigation indicates that the relative error upper bound between the solutions of GM(1,1,W) and GM(1,1,C) is 0.9% when the developing coefficient is within [-1/(n+1),0] and hence the solution of GM(1,1,C) can be replaced reasonably with that of GM(1,1,W). However the relative error between the solutions of these two models may reach 8.64% when the developing coefficient is in [-2/(n+1),0], and so the solution of GM(1,1,C) only can be replaced very cautiously with that of GM(1,1,W).
关键词
白化型GM(1 /
1)模型 /
内涵型GM(1 /
1)模型 /
相对误差上界 /
发展系数 /
单调增长序列
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Key words
whitenization GM(1,1) model /
connotation GM(1,1) model /
relative error upper bound /
developing coefficient /
monotone increasing raw sequence
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中图分类号：
O231
N94
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参考文献
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脚注
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基金
国家自然科学基金(70971103);国家教育部高等学校博士学科点专项科研基金(20120143110001);教育部人文社会科学专项科研基金(11YJC630155)
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