基于Leslie矩阵和时间序列分析的人口预测研究
发布时间：2019-03-14 14:49
【摘要】：线性回归模型、Leslie转移矩阵和属于微分方程方法的Logistic模型是预测人口时经常使用的三种人口预测方法。对人口进行中长期预测时往往采用Leslie矩阵方法，这种方法在上述三种方法中对中长期的人口预测结果精度高，考虑因素多，适合我国现阶段人口预测的需要。时间序列分析的方法处理同种数据所得到的预测结果精确，ARMA模型作为时间序列分析方法中的重要模型，它具有可扩展性强的优点。我们经研究发现将时间序列分析的方法运用到Leslie矩阵中各变量的预测，将二者进行融合，能更好的解决人口预测问题。 本文通过时间序列分析方法对Leslie矩阵中的生育率变量和死亡率变量进行修正，将时间序列分析的方法与Leslie矩阵相结合，，使结合后得到的新模型在进行长期人口预测时得到的预测结果更准确，能够更准确地对长期人口进行预测。在选用时间序列分析方法时，考虑到生育率变量数据构成序列为非平稳时间序列，我们选择对ARMA模型进行了改进，使其能够对生育率变量进行预测。 具体的工作如下： （1）介绍了本文的研究背景、研究目的以及研究意义 总结了近年来时间序列分析方法发展的状况，以及用Leslie矩阵预测人口的现状，并研究了Leslie矩阵和时间序列分析方法结合的现状。 （2）介绍了本文的背景知识 包括Leslie矩阵各项的含义，用Leslie矩阵预测人口的原理。介绍了时间序列分析的相关理论，阐述时间序列分析中的ARMA模型、ARIMA模型。并介绍了人口预测模型中的灰色模型和Logistic模型及其预测原理。 （3）分析时间序列分析中ARMA模型的不足，给出适于分析Leslie矩阵生育率变量的改进ARMA模型 使用Leslie矩阵进行人口预测时，由于假定出生率和死亡率不发生变化，而随着时间的变化，真实的生育率、死亡率和Leslie矩阵中所用的生育率、死亡率的值产生差别。由于这种变化是非线性的，生育率的时间序列又是非平稳的，因此，我们不能够直接使用ARMA模型进行预测。为了解决这一问题，我们改进了ARMA模型，使其能够对非平稳序列进行拟合，对Leslie矩阵中的生育率变量和死亡率变量进行预测。 （4）提出了基于Leslie矩阵和改进ARMA模型的人口预测模型 给出改进后Leslie矩阵预测人口的数据流程。具体的过程，使用改进的ARMA模型预测Leslie矩阵人口生育率变量的变化；直接使用ARMA模型预测Leslie矩阵中的死亡率变量，用改进ARMA模型预测出的生育率与死亡率修正Leslie矩阵。改进后的Leslie矩阵对已知人口进行转移运算，求得下一年的人口数目。之后重复上述过程，算出多年后的人口，得出目标年人口的预测结果。 （5）实验结果比较 通过实验比较改进Leslie模型和灰色模型、Logistic模型在人口预测结果上的比较，验证改进模型在长期人口预测上的优势。 使用传统Leslie矩阵进行人口预测的时候，生育率变量和死亡率变量考虑的不够细致，使得预测的结果不够精确。本文使用改进的ARMA模型对非平稳的生育率变量进行预测，使Leslie矩阵预测得到更准确的结果。 在处理非平稳序列的时候ARMA模型预测的结果会随时间产生较大偏差，本文针对这种情况提出了改进方法，使ARMA模型能够对非平稳时间序列数据进行预测。并通过这种改进预测Leslie矩阵中的生育率与死亡率变量，使改进ARMA方法与Leslie矩阵结合所得模型对人口的长期预测精度提高。
[Abstract]:The linear regression model, the Leslie transfer matrix and the Logistic model of the differential equation method are the three population prediction methods that are often used in the prediction of the population. In the medium and long-term prediction of the population, the Leslie matrix method is often used, and the method has the advantages of high precision of the medium-and long-term population prediction results in the three methods, and more consideration factors, and is suitable for the needs of the population prediction at the present stage in China. The method of time series analysis processes the prediction result obtained by the same data to be accurate, and the ARMA model is an important model in the time series analysis method, and has the advantages of strong expandability. We have found that the method of time series analysis is applied to the prediction of the variables in the Leslie matrix, and the two are fused, and the problem of population prediction can be better solved. In this paper, the time series analysis method is used to revise the fertility and mortality variables in the Leslie matrix, and the time series analysis method is combined with the Leslie matrix, so that the new model obtained after the combination is more accurate in the prediction of the long-term population prediction. in fact, that long-term population can be more accurately pre- In that time series analysis method, the ARMA model was modified to make it possible to prejudge the fertility variable, taking into account that the sequence of the data of the fertility variable was a non-stationary time sequence. A. Specific work. The research background and purpose of this paper are described as follows: (1) and the research significance summarizes the development of the time series analysis method in recent years, as well as the Leslie matrix The present situation of population is predicted, and the Leslie matrix and time series analysis are also studied. The current status of the method. (2) This paper introduces the background knowledge of this paper, including the meaning of Leslie's matrix, and uses Lesl The principle of the population is predicted by the e-matrix. The correlation theory of time series analysis is introduced, and the ARM in the time series analysis is described. A model and ARIMA model are presented. The grey model and Lois in the population prediction model are introduced. (3) analyzing the deficiency of ARMA model in time series analysis, and giving an analysis of Leslie matrix when the improved arma model of the fertility variable uses the Leslie matrix for population prediction, it is assumed that the birth rate and the mortality rate do not change, and as time changes, the real fertility rate, the mortality rate, and the Leslie matrix The value of the fertility rate and the mortality rate is different. Since this change is non-linear, the time series of the fertility rate is non-stationary, so we can't To solve this problem, we improve the ARMA model and make it possible to fit the non-stationary sequence to the Leslie matrix. The fertility variable and the mortality variable are predicted. (4) Based on Leslie The Population Prediction Model of the Matrix and the Improved ARMA Model The data flow of the population is predicted by the Leslie matrix. In the specific process, the modified ARMA model is used to predict the change of the Leslie matrix population fertility variable. The ARMA model is used to predict the mortality variable in the Leslie matrix, and the ARMA model is used to predict the mortality in the Leslie matrix. The modified Leslie matrix for fertility and mortality. The modified Leslie matrix is known The population is transferred, and the population number of the next year is obtained. The above process is repeated and calculated. For many years, the population has come to the conclusion that The results of the population forecast in the target year. (5) The experimental results are compared with the experimental results to improve the Leslie model and the grey model, and the Logistic model is in the population prediction. On the basis of the comparison of the fruit, the advantage of the improved model in the long-term population projection is verified. When the population is predicted using the traditional Leslie matrix, the fertility variable This paper uses the modified ARMA model to change the non-stable fertility rate. The prediction of the amount of the Leslie matrix results in a more accurate result. The results of the ARMA model prediction can result in a large deviation over time when the non-stationary sequence is processed. in the method, the ARMA model can be used for predicting the non-stationary time series data, and the fertility and the mortality variable in the Leslie matrix are predicted through the improvement, so that the improvement of the ARMA method
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：O211.61;C923
本文编号：2440080
[Abstract]:The linear regression model, the Leslie transfer matrix and the Logistic model of the differential equation method are the three population prediction methods that are often used in the prediction of the population. In the medium and long-term prediction of the population, the Leslie matrix method is often used, and the method has the advantages of high precision of the medium-and long-term population prediction results in the three methods, and more consideration factors, and is suitable for the needs of the population prediction at the present stage in China. The method of time series analysis processes the prediction result obtained by the same data to be accurate, and the ARMA model is an important model in the time series analysis method, and has the advantages of strong expandability. We have found that the method of time series analysis is applied to the prediction of the variables in the Leslie matrix, and the two are fused, and the problem of population prediction can be better solved. In this paper, the time series analysis method is used to revise the fertility and mortality variables in the Leslie matrix, and the time series analysis method is combined with the Leslie matrix, so that the new model obtained after the combination is more accurate in the prediction of the long-term population prediction. in fact, that long-term population can be more accurately pre- In that time series analysis method, the ARMA model was modified to make it possible to prejudge the fertility variable, taking into account that the sequence of the data of the fertility variable was a non-stationary time sequence. A. Specific work. The research background and purpose of this paper are described as follows: (1) and the research significance summarizes the development of the time series analysis method in recent years, as well as the Leslie matrix The present situation of population is predicted, and the Leslie matrix and time series analysis are also studied. The current status of the method. (2) This paper introduces the background knowledge of this paper, including the meaning of Leslie's matrix, and uses Lesl The principle of the population is predicted by the e-matrix. The correlation theory of time series analysis is introduced, and the ARM in the time series analysis is described. A model and ARIMA model are presented. The grey model and Lois in the population prediction model are introduced. (3) analyzing the deficiency of ARMA model in time series analysis, and giving an analysis of Leslie matrix when the improved arma model of the fertility variable uses the Leslie matrix for population prediction, it is assumed that the birth rate and the mortality rate do not change, and as time changes, the real fertility rate, the mortality rate, and the Leslie matrix The value of the fertility rate and the mortality rate is different. Since this change is non-linear, the time series of the fertility rate is non-stationary, so we can't To solve this problem, we improve the ARMA model and make it possible to fit the non-stationary sequence to the Leslie matrix. The fertility variable and the mortality variable are predicted. (4) Based on Leslie The Population Prediction Model of the Matrix and the Improved ARMA Model The data flow of the population is predicted by the Leslie matrix. In the specific process, the modified ARMA model is used to predict the change of the Leslie matrix population fertility variable. The ARMA model is used to predict the mortality variable in the Leslie matrix, and the ARMA model is used to predict the mortality in the Leslie matrix. The modified Leslie matrix for fertility and mortality. The modified Leslie matrix is known The population is transferred, and the population number of the next year is obtained. The above process is repeated and calculated. For many years, the population has come to the conclusion that The results of the population forecast in the target year. (5) The experimental results are compared with the experimental results to improve the Leslie model and the grey model, and the Logistic model is in the population prediction. On the basis of the comparison of the fruit, the advantage of the improved model in the long-term population projection is verified. When the population is predicted using the traditional Leslie matrix, the fertility variable This paper uses the modified ARMA model to change the non-stable fertility rate. The prediction of the amount of the Leslie matrix results in a more accurate result. The results of the ARMA model prediction can result in a large deviation over time when the non-stationary sequence is processed. in the method, the ARMA model can be used for predicting the non-stationary time series data, and the fertility and the mortality variable in the Leslie matrix are predicted through the improvement, so that the improvement of the ARMA method
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：O211.61;C923
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