Discussions of the Mathematical Mechanism for Constructing the GM (1, 1) Model

Abstract

Starting from analyzing dynamic characteristics of the general energy system, this article discusses the mathematical mechanism of the GM (1, 1) model for producing AGO/IAGO data and the mathematical mechanism for constructing “the model equation” and the mathematical mechanism for parameter estimation. It also discusses other aspects of the application of the GM (1, 1) model. It points out: A. the classic GM (1, 1) model follows the principle of RMI model, but there exist background defects of the "planning predictions" and internal discords of the model caused by the prior assumptions in which both development coefficient and gray effective amount are constant, which restricts the application of the model. B. The classic GM (1, 1) model, in principle, only applies to fitting modeling of time sequences which tend to be slow and with wider intervals and positive stable values. C. Gray differential equation as a tool for estimating the parameters is not indispensible, so this article suggests optimizing parameter calculation method: gray differential equation providing initial iteration, using the end of AGO generating sequence as the boundary condition, etc. to improve the precision and explicability of the GM (1, 1) model.