NDGM模型的性质及预测效果分析

在近似非齐次指数序列的离散灰色模型（non-homogenous discrete grey model, NDGM）基础上研究了该模型的参数特性，分析了仿射变换导致的模型参数变化特征，结果表明,变换前后所得预测值仍然具有仿射变换关系，验证了NDGM模型对非齐次指数序列预测的无偏性。通过求解NDGM模型，给出针对一般指数序列的完全拟合表达式，并给出了求解近似指数序列最优拟合表达式的算法步骤。最后以1999年~2008年我国人均国内生产总值为例进行模拟和分析，验证了该方法在离散灰色预测中的可行性。

Research on properties of non-homogenous discrete grey model and its predictive results

To study the properties of non-homogenous discrete grey model （NDGM）, the variation characteristics of several model parameters pertaining to affine transformation are analyzed thoroughly. The predictive results from the series of analyses demonstrate the retaining affine property between carefully manipulated primary sequence and its affine sequence-the replica of each sequence is added to the original sequence. In addition, the analyses verify the fact that the non-homogenous discrete grey model is competent and valid for perfect simulation on the non-homogenous sequence. The completely fitting expression of general exponential sequence and the optimized fitting expression of approximative exponential sequence are proposed by solving the non-homogenous discrete grey model. In this study, an algorithmic approach for the non-homogenous discrete grey model is also suggested and briefly discussed. China’s per-capita GDP from 1992 to 2008 is employed as an example to further explicate the algorithmic approach of the non-homogenous discrete grey model. As such, the approach is proven to be effective and feasible.