Equivalency and unbiasedness of grey prediction models  

作　　者：Bo Zeng Chuan Li Guo Chen Xianjun Long 

机构地区：[1]College of Business Planning, Chongqing Technology and Business University [2]School of Management and Economics, University of Electronic Science and Technology [3]Chongqing Key Laboratory of Manufacturing Equipment Mechanism Design and Control [4]School of Electrical & Information Engineering, University of Sydney [5]College of Mathematics & Statistics, Chongqing Technology and Business University

出　　处：《Journal of Systems Engineering and Electronics》2015年第1期110-118,共9页系统工程与电子技术（英文版）

基　　金：supported by the National Natural Science Foundation of China(11471059;51375517;71271226);the China Postdoctoral Science Foundation Funded Project(2014M560712);Chongqing Frontier and Applied Basic Research Project(cstc2014jcyj A00024);the Ministry of Education of Humanities and Social Sciences Youth Foundation(14YJAZH033);the Chongqing Municipal Education Scientific Planning Project(2012-GX-142);the Higher School Teaching Reform Research Project in Chongqing(1202010)

摘　　要：In order to deeply research the structure discrepancy and modeling mechanism among different grey prediction models, the equivalence and unbiasedness of grey prediction models are analyzed and verified. The results show that all the grey prediction models that are strictly derived from x^（0）（k） ＋az^（1）（k） = b have the identical model structure and simulation precision. Moreover, the unbiased simulation for the homogeneous exponential sequence can be accomplished. However, the models derived from dx^（1）/dt ＋ ax^（1）= b are only close to those derived from x^（0）（k） ＋ az^（1）（k） = b provided that ｜a｜ has to satisfy｜a｜ 0.1; neither could the unbiased simulation for the homogeneous exponential sequence be achieved. The above conclusions are proved and verified through some theorems and examples.In order to deeply research the structure discrepancy and modeling mechanism among different grey prediction models, the equivalence and unbiasedness of grey prediction models are analyzed and verified. The results show that all the grey prediction models that are strictly derived from x^（0）（k） ＋az^（1）（k） = b have the identical model structure and simulation precision. Moreover, the unbiased simulation for the homogeneous exponential sequence can be accomplished. However, the models derived from dx^（1）/dt ＋ ax^（1）= b are only close to those derived from x^（0）（k） ＋ az^（1）（k） = b provided that ｜a｜ has to satisfy｜a｜ 0.1; neither could the unbiased simulation for the homogeneous exponential sequence be achieved. The above conclusions are proved and verified through some theorems and examples.

关 键 词：system modeling grey prediction models equivalency and unbiasedness 

分 类 号：C91[经济管理]