论文总字数：18104字

摘 要

本文在选取合适的人口数据后，利用SAS软件，得出ARIMA(0,2,(1,3))疏系数模型能够较好的拟合我国目前的人口趋势，且新冠病情对我国人口影响在模型误差之内。模型预测显示:我国人口从1962年增长至今，增长速度趋近平缓，保持一个稳定的增长趋势。模型预测了我国2020年-2025年的人口。

本文第一章是引言。第一节阐述了论文研究的目的和意义即人口发展问题是社会发展的重要因素并预测我国未来5内年的人口总数。第二节介绍了ARIMA模型的原理及模型的表达式和参数意义。第三节则是数据的筛选，在数据处理后，选取了我国1962-2019年人口总数为模型的研究对象，并解释了筛选的理由。

本文第二章是文献综述，介绍了国内外研究现状，重点讨论了与人口数量相关的因素，比如:育龄妇女生育率，总和生育率，人口净增长率，性别比例，死亡率和出生率，人口密度，人口总数。综述了人口预测的1阶差分模型，ARIMA模型，指数平滑模型，回归模型。

本文第三章是建模和检验。第一节在SAS软件中建立原时序图和差分后时序图，排除了原序列和1阶差分序列的建模可能。第二节对2阶差分序列做相关性检验，确定了其平稳性。第三节对2阶差分序列做纯随机性检验，确定存在建模意义。第四节使用最小二乘估计来确定模型的p，q阶数。第五节对预定的p，q组合的模型做参数检验对比选取拟合效果最好的组合。第六节对序列做残差自相关检验，确定无可提取信息，即模型不需要改进。第七节对确定的组合做参数估计确定模型的参数，得到最终模型。

本文第四章是模型的预测，第一节是利用模型对我国2020-2024年人口的预测。第二节是对目前新冠疫情对我国人口进程的影响的分析，疫情死亡人数小于误差的百分之一，确认对模型无影响。

关键词: 人口预测 2阶差分 ARIMA模型

The recurrence relation method of population projections

Abstract

In this thesis, after selecting suitable population data, using SAS software,the Arima (0,2,(1,3)) sparse coefficient model can fit the current population trend of our country well, and the effect of new crown disease on the population of our country is within model error.The model forecast shows that the population of China has increased from 1962 to the present, with the growth rate tending to moderate and maintaining a stable growth trend. The model forecast that the population of China in 2020 to 2024。

The first chapter of this thesis is the introduction. The First Section describes the purpose of the thesis: short-term forecasting of China's population from 2020-2024. The second section， show the Arima model's principle, expression and parameter significance . The third section is the data screening, after the data processing, selected China's population from 1962 to 2019 as the model of the research object, and explained the reasons for the screening.

The second chapter of this thesis is literature review.This thesis introduces the present research situation at home and abroad, and mainly discusses the factors related to population quantity,such as : Fertility rate of women of childbearing age, total fertility rate, net population growth rate, sex ratio, mortality and birth rate, population density, total population. This thesis summarizes the 1-order difference model, Arima model, exponential smoothing model and regression model of population forecasting.

The third chapter of this thesis is modeling and verification. In the first section, the original sequence diagram and the differential post-sequence diagram are established in SAS, which eliminates the possibility of modeling the original sequence and the first-order differential sequence. In the Second Section, we test the correlation of the second order difference sequence and determine its stationarity. In the third section, we test the pure randomness of the 2-order difference series to confirm the existence of modeling significance. The fourth section uses the least square estimation to determine the P, q order of the model. In the fifth section, we choose the combination with the best fitting effect by comparing the parameters of the prearranged P and q combination. In the sixth section, the residual autocorrelation test is done to confirm that there is no extractable information, that is, the model does not need to be improved. In the seventh section, we estimate the parameters of the model and get the final model Arima (0,2,(1,3)).

The Fourth Chapter of this thesis is model prediction and analysis, the First Section, using the model to predict the total population of China from 2020 to 2024. In the second section, the impact of the new crown disease on the population process in China is analyzed. The death rate is less than 1% of the error.

Key words: Population projections; Second order difference; ARIMA model

目 录

摘要……………………………………………………………………………………I

ABSTRACT……………………………………………………………………………II

第一章 引言…………………………………………………………………………1

1.1课题意义…………………………………………………………………………1

1.2模型原理…………………………………………………………………………1

1.3数据的选取………………………………………………………………………1

第二章 文献综述……………………………………………………………………4

2.1国内外研究现状…………………………………………………………………4

2.2国内外研究现状…………………………………………………………………6

第三章 建模和检验…………………………………………………………………7

3.1 建立时序图 ……………………………………………………………………7

3.2 相关性检验……………………………………………………………………8

3.3 纯随机性检验…………………………………………………………………8

3.4 条件最小二乘估计……………………………………………………………9

3.5 参数估计和互相关检验………………………………………………………10

3.6 残差检验与分析………………………………………………………………11

3.7 最终模型参数估计……………………………………………………………12

第四章模型预测与分析……………………………………………………………13

4.1模型预测………………………………………………………………………13

4.2浅谈新冠病毒影响……………………………………………………………14

结语…………………………………………………………………………………15

参考文献……………………………………………………………………………15

附录…………………………………………………………………………………18

请支付后下载全文，论文总字数：18104字