广义离散灰色预测模型及其应用

基于离散灰色预测模型提出了广义离散灰色预测模型(GDGM(1,1)模型),它包含了常见的齐次与非齐次指数序列模型,一次累加抛物型自回归模型,以及一次累加时变线性模型;证明了对四类特殊序列具有模拟完全重合性;研究了在数乘变化下模型参数与模拟值的变化规律以及相对误差的不变性;给出了模型建模步骤及其方法,通过实例对DGM(1,1)模型,NDGM(1,1)模型,CDGM(1,1)模型,TDGM(1,1)模型,NHGM(1,1,k)模型,GM(1,1)直接建模模型以及本文模型的模拟预测效果进行了比较,结果表明GDGM(1,1)模型能够提高预测模拟精度.

Generalized discrete grey model and its application

Based on the discrete grey prediction model, the generalized discrete grey prediction model (GDGM(1,1) model) is proposed, which includes the common homogeneous and non-homogeneous exponential series model, the order first cumulative parabolic autoregressive model, and the first cumulative time-varying linear model. It is proved that the simulation coincidence of four special sequences is perfect. The variation law of model parameters and simulated values and the invariance of relative errors under the multiplication of numbers are studied. The modeling steps and methods of this model are given, and the simulation and prediction results of DGM(1,1), NDGM(1,1), CDGM(1,1), TDGM(1,1), NHGM(1,1,k), GM (1,1) direct modeling method and this model are compared by examples, the results show that GDGM(1,1) can improve the accuracy of simulation prediction.