A Direct Modeling Method of the Unbiased GM(1,1)

Abstract

There are some problems in GM( 1,1) modeling, such as, modeling method biased, compatibility condition not satisfied , linear transformation inconsistent and the first number of the initial sequence not functioning in modeling after an accumulated generating operation. In this paper, three grey differential equations are presented and a direct modeling method of the unbiased CM (1,1) is proposed.It is proved that the new method possesses not only white exponential law coincidence property but also linear transformation consistency. The analysis of practical examples show that it improves the modeling precision, enlarges the application scope of the model and makes full use of the first number of the initial sequence.