基于最小二乘法的GM(1,1)模型在人口预测中的应用

作者先对问题进行分析,在明白要采取灰色系统理论来处理该问题原因的前提下,运用普通的GM(1,1)模型的知识,通过优化GM(1,1)模型(下称模型一)、新陈代谢GM(1,1)模型(下称模型二),鉴于此,采用最小二乘法对模型一和模型二预测出的两组数据,以及实际数据进行拟合,得到了关于模型一,模型二的两个系数,然后用这样的两个系数,重新组合模型一,模型二,得到了第三个模型,即基于最小二乘法的GM(1,1)模型(下称模型三),再一次的进行预测。三个模型的预测数据进行比较,显然是模型三的误差最小,认为模型三最符合实际。并以基于最小二乘法的GM(1,1)模型的预测数据作为最终的结果。

The problem on forecasting the total population in China——The improved GM(1,1) model applied in forcasting population

In this paper we analyse the problem at first.Before we understand that we need to use Grey Theory to solve this problem.We use common GM(1,1),througing optional GM(1,1)(model one),metabolism GM(1,1)(model two).Because of this,we fit practical data which is forecasted by model one and model two through the least square method.We can gain the coefficients of model 1 and model 2.And then we use these two coefficients.Recombinant model 1 and model 2.We can gain the third model.This is GM(1,1) model which is gained by the least square method.(model three).Then forecast again.We compare the three kinds of data which are forecasted by these three models.Obviously,the error of the model 3 is the least.We think model 3 is accorded with the fact.And we use the data which is forecasted by the improved GM(1,1)as the last result.