Research on MGM (1,N|τ,r) model and its application

In accordance with the characteristics of the complex system, its multivariable, nonlinear and delayed, based on MGM (1, N), this paper proposes a new multivariable grey model (MGM (1, N|τ, r)) which is established by introducing delayed factor τ and nonlinear factor r. The main work of this article is to research modeling process, parameter estimation, precision inspection, forecasting and so on. During modeling, the particle swarm optimization (PSO) algorithem is used to solve the parameters τ, r. Finally, MGM (1, N|τ, r) is applied for forecasting input and output of Wuhan new hi-tech industry. By comparing the forecast results of MGM (1, N|τ, r) and mgm(1, n), we can obtain that the new model possesses a much higher precision and grey correlation degree. MGM (1, N|τ, r) is a reasonable and effective method to resolve the delayed and nonlinear system.