近似非齐次指数增长序列的间接DGM（1,1）模型分析

DGM（1,1）模型对近似齐次指数增长序列具有较高的预测精度,而实际上服从近似齐次指数增长规律的数据序列十分有限。根据灰色系统理论的差异信息原理,通过原始序列的累减生成将近似非齐次指数增长序列转化为近似齐次指数增长序列,对累减生成序列建立DGM（1,1）模型,并在此基础上实现对原始序列的还原以达到数据模拟及预测之目的。因原始序列的累减生成最大可能地满足了建模序列的齐次性要求,提高了模拟及预测精度,拓展了模型的适用范围,故通过算例验证了此种改进方法的简单性、实用性及有效性。

Analysis of Indirect DGM (1, 1) Model of Non-Homogeneous Exponential Incremental Sequences

The precision,with applying the DGM（1,1）model to forecast a homogeneous exponential incremental sequence,is satisfactory;however,incremental sequences which are approximate to meet the homogeneous exponential distribution are very limited.According the principle of informational differences in grey system theory,a non-homogeneous exponential incremental sequence may be converted into a homogeneous one through inverse accumulating generator of a raw sequence,next,a model of DGM（1,1） is built by the new sequence,and then,after reverting to the original sequence,it can accomplish the targets of simulation and prediction for the raw sequence.An indirect DGM（1,1）model,with approximately meeting the homogeneity demand of a modeling sequence by the greatest possible degree,improves the precision of simulation and prediction,extends the range of application of the raw DGM.Ultimately,two examples show the simplicity,practicability and validity of the improved approach.