基于可变生成系数的灰色模型GM(1,1)及其应用

Grey Model GM(1,1)Based on Variable Generation Coefficient and Its Applications

在灰色预测中,GM(1,1)模型得到广泛的应用,但传统的GM(1,1)模型预测有时误差较大,其原因是来自对模型背景值的近似。文章基于可变生成系数的背景值优化从模型的参数估计上进行改进,主要采用了两种改进方法:一是基于背景值生成系数为不等权常数改进模型;二是基于背景值生成系数为不等权变数改进模型。由改进的方法对中国房地产业经济增长建立了GM(1,1)模型,结果表明,利用改进的方法使GM(1,1)模型预测精度显著提高。

The GM(1,1)model is widely used in grey prediction,but the traditional GM(1,1)model sometimes has a large prediction error because of the approximation of the background value of the model.This paper improves the parameter estimation of the model based on the optimization of background value with variable generation coefficient,mainly adopting two improvement methods:One is to improve the model based on the unequal weight constant of the generating coefficient of the background value;the other is based on the background value to generate coefficients for unequal weight variables to improve the model.Finally,the paper uses the improved method to establish a GM(1,1)model.The results show that the improved method significantly improves the accuracy of the model.