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Application of Grey Model in the Aging Population Forecast in Chongqing
DOI: 10.12677/AAM.2019.87145, PDF, HTML, XML, 下载: 1,073  浏览: 8,687

Abstract: According to the statistical yearbook data of Chongqing in 2008-2017, the grey forecasting model is used to predict the aging population in Chongqing in the next decade. It is predicted that the population aged 65 and over will reach 5.1103 million in 2027, and the aging coefficient will in-crease year by year. Therefore, the degree of aging continues to increase.

1. 引言

2. 灰色GM(1,1)模型的建立

2.1. 灰色GM(1,1)模型的建立

${X}^{\left(0\right)}=\left\{{X}^{\left(0\right)}\left(1\right),{X}^{\left(0\right)}\left(2\right),\cdots ,{X}^{\left(0\right)}\left(n\right)\right\}$ 是原始数据序列，对 ${X}^{\left(0\right)}$ 进行一次累加生成，得到累加生成序列 ${X}^{\left(1\right)}=\left\{{X}^{\left(1\right)}\left(1\right),{X}^{\left(1\right)}\left(2\right),\cdots ,{X}^{\left(1\right)}\left(n\right)\right\}$ ，其中 ${X}^{\left(1\right)}\left(t\right)=\underset{i=1}{\overset{t}{\sum }}{X}^{\left(0\right)}\left(i\right)$$t=1,2,\cdots ,n$

$\left\{\begin{array}{l}\frac{\text{d}{X}^{\left(1\right)}\left(t\right)}{\text{d}t}+a{X}^{\left(1\right)}\left(t\right)=u\\ {X}^{\left(1\right)}\left(1\right)={X}^{\left(0\right)}\left(1\right)\end{array}$

$\stackrel{^}{a}={\left[a,u\right]}^{\text{T}}={\left({B}^{\text{T}}B\right)}^{-1}{B}^{\text{T}}Y$

${\stackrel{^}{X}}^{\left(1\right)}\left(t+1\right)=\left({X}^{\left(0\right)}\left(1\right)-\frac{u}{a}\right){\text{e}}^{-at}+\frac{u}{a}$$t=1,2,\cdots ,n$

${\stackrel{^}{X}}^{\left(0\right)}\left(t+1\right)={\stackrel{^}{X}}^{\left(1\right)}\left(t+1\right)-{\stackrel{^}{X}}^{\left(1\right)}\left(t\right)$$t=1,2,\cdots ,n$

2.2. 模型精度的检验 [3]

1) 残差检验

2) 后验差检验

Table 1. Posterior accuracy standard

3. 利用灰色模型预测重庆市老龄化人口 [4] [5]

3.1. 研究区概况

3.2. 数据收集

Table 2. Statistical table of total population, population aged 65 and above and aging coefficient of Chongqing from 2008 to 2017

3.3. 重庆市老龄化人口预测

Table 3. Grey G M ( 1 , 1 ) model prediction value and relative error (ten thousand people)

Table 4. Prediction of population aged 65 and above and aging coefficient in Chongqing from 2018 to 2027

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