﻿ 安徽省人口老龄化程度预测研究

# 安徽省人口老龄化程度预测研究Population Aging Degree Prediction Research in Anhui Province

Abstract: China has large population, the population issue has become an important reason for restricting China’s economic development. Anhui Province is the country’s most populated province, and in 1998, it entered the aging society. Due to the continued increase in the aging population, aging population has brought increasingly serious social, economic and other important problems. Therefore, the development of aging research and analysis without delay, to accurately predict the trend of population aging, and the stability of the socio-economic development of Anhui Province, is particularly important. This paper uses part of the data in1998~2015 in Anhui Province relating to the elderly population and the gray forecast GM(1,1) model prediction methods to predict the total population in Anhui Province and elderly population over the next decade, and then forecast the aging factor. The results showed that the total population in Anhui Province will continue to rise in next decade, and elderly population is also in the process of increasing, population aging coefficient subsequently continues to rise. Finally, according to the empirical model, the current situation and forecast results of Anhui population aging are analyzed and related policy recommendations are presented based on the results.

1. 引言

2. 安徽省人口老龄化发展历程及成因

2.1. 安徽省人口老龄化发展历程

2.2. 安徽省人口老龄化成因

3. 预测方法的选择

3.1. 灰色预测法定义

3.2. 灰色预测模型的建立

${X}^{\left(1\right)}=\left\{{X}^{\left(1\right)}\left(1\right),{X}^{\left(1\right)}\left(2\right),\cdots ,{X}^{\left(1\right)}\left(n\right)\right\}$ (1)

$\frac{\text{d}{X}^{\left(1\right)}}{\text{d}t}+a{X}^{\left(1\right)}=\mu$ (2)

$\stackrel{^}{\alpha }$ 为待估参数向量， $\stackrel{^}{\alpha }=\left(\frac{a}{\mu }\right)$ ，可用最小二乘法求解，可得 $\stackrel{^}{\alpha }={\left({B}^{\text{T}}B\right)}^{-1}{B}^{\text{T}}{Y}_{n}$ ，其中，

$B=\left[\begin{array}{cc}-1/2\left[{X}^{\left(1\right)}\left(1\right)+{X}^{\left(1\right)}\left(2\right)\right]& 1\\ -1/2\left[{X}^{\left(1\right)}\left(2\right)+{X}^{\left(1\right)}\left(3\right)\right]& 1\\ ⋮& ⋮\\ -1/2\left[{X}^{\left(1\right)}\left(n-1\right)+{X}^{\left(1\right)}\left(n\right)\right]& 1\end{array}\right]$ , ${Y}_{n}=\left[\begin{array}{c}{X}^{\left(0\right)}\left(2\right)\\ {X}^{\left(0\right)}\left(3\right)\\ ⋮\\ {X}^{\left(0\right)}\left(N\right)\end{array}\right]$

${\stackrel{^}{X}}^{\left(1\right)}\left(k+1\right)=\left[{X}^{\left(0\right)}\left(1\right)-\frac{\mu }{a}\right]{\text{e}}^{-ak}+\frac{\mu }{a}$ ( $k=0,1,2,\cdots ,n$ )(3)

3.3. 模型的检验

${\Delta }^{\left(0\right)}\left(i\right)=|{X}^{\left(0\right)}\left(i\right)-{\stackrel{^}{X}}^{\left(0\right)}\left(i\right)|$ , $i=1,2,\cdots ,n$

$\varphi \left(i\right)=\frac{{\Delta }^{\left(0\right)}\left(i\right)}{{X}^{\left(0\right)}\left(i\right)}×100%$ , $i=1,2,\cdots ,n$

1) 计算原始序列的标准差： ${S}_{1}=\sqrt{\frac{\sum {\left[{X}^{\left(0\right)}\left(i\right)-{\stackrel{¯}{X}}^{\left(0\right)}\right]}^{2}}{n-1}}$

2) 计算绝对误差序列的标准差： ${S}_{2}=\sqrt{\frac{\sum {\left[{\Delta }^{\left(0\right)}\left(i\right)-{\stackrel{¯}{\Delta }}^{\left(0\right)}\right]}^{2}}{n-1}}$

3) 计算方差比： $C=\frac{{S}_{2}}{{S}_{1}}$

4) 计算小误差概率： $P=P\left\{|{\Delta }^{\left(0\right)}\left(i\right)-{\stackrel{¯}{\Delta }}^{\left(0\right)}|<0.6745{S}_{1}\right\}$

${e}_{i}=|{\Delta }^{\left(0\right)}\left(i\right)-{\stackrel{¯}{\Delta }}^{\left(0\right)}|$${S}_{0}=0.6745{S}_{1}$ ，则 $P=P\left\{{e}_{i}<{S}_{0}\right\}$

4. 模型建立、预测结果及分析

4.1. 样本选取和数据说明

Table 1. Accuracy inspection level reference table [2]

Table 2. Population ageing in Anhui Province from 1998 to 2015

4.2. 安徽省人口总数以及老年人口数GM(1,1)模型建立

$\begin{array}{l}{x}^{\left(0\right)}=\left(6152,6205,6278,6325,6369,6410,6461,6516,6593,6676,\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}6741,6795,6827,6876,6902,6929,6936,6949\right)\end{array}$

${\stackrel{^}{x}}^{\left(1\right)}\left(k+1\right)=829032{\text{e}}^{0.0075k}+822880$ (4)

Table 3. Results of total population forecast for Anhui Province from 1998 to 2015

$\begin{array}{l}{x}^{\left(0\right)}=\left(431.87,457.93,476.50,512.33,541.37,589.08,600.87,656.81,669.85,\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}715.67,751.62,776.67,698.40,784.55,833.76,848.11,812.21,815.12\right)\end{array}$

${\stackrel{^}{x}}^{\left(1\right)}\left(k+1\right)=14162.37{\text{e}}^{0.0351k}+13730.5$ (5)

4.3. 预测结果与分析

Table 4. Results of the elderly population in Anhui Province from 1998 to 2015

Table 5. Forecast results of population aging in Anhui Province from 2016 to 2025

5. 结论与相关政策建议

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