基于Leslie矩陣和時間序列分析的人口預(yù)測研究
發(fā)布時間：2019-03-14 14:49
【摘要】：線性回歸模型、Leslie轉(zhuǎn)移矩陣和屬于微分方程方法的Logistic模型是預(yù)測人口時經(jīng)常使用的三種人口預(yù)測方法。對人口進行中長期預(yù)測時往往采用Leslie矩陣方法，這種方法在上述三種方法中對中長期的人口預(yù)測結(jié)果精度高，考慮因素多，適合我國現(xiàn)階段人口預(yù)測的需要。時間序列分析的方法處理同種數(shù)據(jù)所得到的預(yù)測結(jié)果精確，ARMA模型作為時間序列分析方法中的重要模型，它具有可擴展性強的優(yōu)點。我們經(jīng)研究發(fā)現(xiàn)將時間序列分析的方法運用到Leslie矩陣中各變量的預(yù)測，將二者進行融合，能更好的解決人口預(yù)測問題。 本文通過時間序列分析方法對Leslie矩陣中的生育率變量和死亡率變量進行修正，將時間序列分析的方法與Leslie矩陣相結(jié)合，，使結(jié)合后得到的新模型在進行長期人口預(yù)測時得到的預(yù)測結(jié)果更準(zhǔn)確，能夠更準(zhǔn)確地對長期人口進行預(yù)測。在選用時間序列分析方法時，考慮到生育率變量數(shù)據(jù)構(gòu)成序列為非平穩(wěn)時間序列，我們選擇對ARMA模型進行了改進，使其能夠?qū)ι首兞窟M行預(yù)測。 具體的工作如下： （1）介紹了本文的研究背景、研究目的以及研究意義 總結(jié)了近年來時間序列分析方法發(fā)展的狀況，以及用Leslie矩陣預(yù)測人口的現(xiàn)狀，并研究了Leslie矩陣和時間序列分析方法結(jié)合的現(xiàn)狀。 （2）介紹了本文的背景知識 包括Leslie矩陣各項的含義，用Leslie矩陣預(yù)測人口的原理。介紹了時間序列分析的相關(guān)理論，闡述時間序列分析中的ARMA模型、ARIMA模型。并介紹了人口預(yù)測模型中的灰色模型和Logistic模型及其預(yù)測原理。 （3）分析時間序列分析中ARMA模型的不足，給出適于分析Leslie矩陣生育率變量的改進ARMA模型 使用Leslie矩陣進行人口預(yù)測時，由于假定出生率和死亡率不發(fā)生變化，而隨著時間的變化，真實的生育率、死亡率和Leslie矩陣中所用的生育率、死亡率的值產(chǎn)生差別。由于這種變化是非線性的，生育率的時間序列又是非平穩(wěn)的，因此，我們不能夠直接使用ARMA模型進行預(yù)測。為了解決這一問題，我們改進了ARMA模型，使其能夠?qū)Ψ瞧椒�(wěn)序列進行擬合，對Leslie矩陣中的生育率變量和死亡率變量進行預(yù)測。 （4）提出了基于Leslie矩陣和改進ARMA模型的人口預(yù)測模型 給出改進后Leslie矩陣預(yù)測人口的數(shù)據(jù)流程。具體的過程，使用改進的ARMA模型預(yù)測Leslie矩陣人口生育率變量的變化；直接使用ARMA模型預(yù)測Leslie矩陣中的死亡率變量，用改進ARMA模型預(yù)測出的生育率與死亡率修正Leslie矩陣。改進后的Leslie矩陣對已知人口進行轉(zhuǎn)移運算，求得下一年的人口數(shù)目。之后重復(fù)上述過程，算出多年后的人口，得出目標(biāo)年人口的預(yù)測結(jié)果。 （5）實驗結(jié)果比較 通過實驗比較改進Leslie模型和灰色模型、Logistic模型在人口預(yù)測結(jié)果上的比較，驗證改進模型在長期人口預(yù)測上的優(yōu)勢。 使用傳統(tǒng)Leslie矩陣進行人口預(yù)測的時候，生育率變量和死亡率變量考慮的不夠細致，使得預(yù)測的結(jié)果不夠精確。本文使用改進的ARMA模型對非平穩(wěn)的生育率變量進行預(yù)測，使Leslie矩陣預(yù)測得到更準(zhǔn)確的結(jié)果。 在處理非平穩(wěn)序列的時候ARMA模型預(yù)測的結(jié)果會隨時間產(chǎn)生較大偏差，本文針對這種情況提出了改進方法，使ARMA模型能夠?qū)Ψ瞧椒�(wěn)時間序列數(shù)據(jù)進行預(yù)測。并通過這種改進預(yù)測Leslie矩陣中的生育率與死亡率變量，使改進ARMA方法與Leslie矩陣結(jié)合所得模型對人口的長期預(yù)測精度提高。
[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
【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：O211.61;C923
本文編號：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
【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：O211.61;C923
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