灰色预测中GM模型的累加生成问题

On the Accumulation Formation of the GM in Grey Prediction

构造灰色模型ＧＭ时，原始数据的累加生成是一个十分重要的概念．分析了累加生成的过程，结果表明：累加生成后数列的权系数服从杨辉三角形（帕斯卡三角形）规律，这说明累加次数越多，旧结息的权重越大，遂使累加生成后数列依扬辉三角的单调升规律变化，这就是累加生成弱化原始数列随机性的本质．指出，用一阶微分方程作为予测模型时必然存在着原理性误差．

Accumulation formation of the original data is a important concept in grey theory.This paper analyses the process of accumulation formation.It is shown that the weight coefficients of the formed serial numbers obey the law of Pascals triangle,that is,the more the number of times of accmulation,the greater the weight of old information.This is the essence that accumulation formation weakens the randomness of the original number series.It is pointed out that there is a inevitable error when differential equation of the first order is taken as prediction model.