Abstract

The gray GM (1 N) model is an important type of prediction model. However, the conventional model’s prediction method has the following two defects: first, the model’s parameter estimate is the approximate value; second, the model’s time response equation has the approximation solution. Because the gray GM (1, N) model involves the multivariable time sequence, the variables form a whole through mutual restrictions and connections. In other words, variables affect each other. The relationship can’t be properly reflected by the conventional gray GM (1, N) model of which the whitening equation is a single differential equation. Therefore, the article proposes a new modeling method which, through simultaneous differential equations, introduces the background values of multiple variables and derives simultaneous gray differential equations to estimate the model’s parameters, and then gets the exact solution of gray GM (1, N) model from the simultaneous whitening equations. The example shows that the model built with the method proposed has the simulation precision and prediction precision significantly higher than that of conventional gray GM (1, N) model. The new method given enriches the system of gray building method and has important significance for the in-depth research, popularization and application of gray model.