向量灰色模型的建立及应用

The Vector Grey Model and Its Application

针对传统多变量灰色预测模型(MGM(1,m))有时存在的建模数据失真问题,以系统中关联变量具有趋同性为基础,提出了一种新的模型--向量灰色模型(VGM(1,m))。与MGM(1,m)模型相比,VGM(1,m)结构更简单,模型参数更少,从而有利于参数的估计。将VGM(1,m)、MGM(1,m)、GM(1,1)模型应用于四个实例的分析,结果表明VGM(1,m)消除了MGM(1,m)的建模失真现象,模型的稳定性得到了增强。进一步,与GM(1,1)建模结果相比,VGM(1,m)模型的预测精度更高,即新模型有更好的泛化性。

When modeling actual data sets by the traditional multivariable grey forecasting model(abbreviated as MGM(1,m)), the simulated data are distorted at times, such that the simulated value is two times that of the true value, and the simulated value is negative while the true value is positive. In order to solve the distortion problem, a new model called the vector grey model(abbreviated as VGM(1,m)) is proposed based on the interrelated variables in the system. Compared with MGM(1,m)model, the VGM(1,m)structure is simpler and the model parameters are less, which is beneficial to the estimation of parameters. So, the amount of parameters calculation in VGM(1,m)is far less than that of MGM(1,m), and the multiple collinear and over fitting phenomena may be alleviated. With four actual examples included air quality index system, economic and energy system, rural household income system and total social fixed investment and gross domestic product(abbreviated as GDP), the results show that VGM(1,m)eliminates the distortion phenomenon which happens in MGM(1,m), so the stability of new model is enhanced. Meanwhile, the prediction accuracy of VGM(1,m)model is higher than GM(1,1)model, which denotes the new model possesses better generalization ability. The new model has expanded the existing grey prediction model system.