Research Of Population Prediction Based On Leslie Matirx And Time Series Analysis

Linear regression model, Leslie matrix and Logistic model which belong to differentialequation method are methods usually used in population forecasting. Leslie matrix method iswidely used in long term population forecasting for it has a better result in the three in longterm population forecasting. It combines lots of factors that affect the population. And it canperform well on Chinese population forecasting recently. Time series analysis method predictswell when dealing with only one type of data. ARMA method is a major method of time seriesanalysis method. It can be transferred to fit specified situation. We find that when we use timeseries analysis method into Leslie matrix we can get a better result when we solve populationforecasting problems.Here we use time series analysis method to forecast the berth rate and death rate of Lesliematrix. We combine time series analysis method and Leslie matrix and get a better result inlong-term population forecasting. We figure that the berth rate of Leslie matrix is non-smoothtime series when we choose which kind of time series analysis method we should use. Thenwe modified ARMA model to let it fit the non-smooth series and predict the berth rate.Our work is as follows:1. We introduce the background, purpose and significance of this research, summarize thedevelopment of Time Series Analysis and analyze the current situation of Leslie Matrixforecasting. And we study the recent combination of Leslie Matrix and time series analysis;2. We introduce the background knowledge. We introduce the variety of Leslie Matrixand how Leslie Matrix works. We introduce time series analysis here too. Further more, weintroduce ARMA and ARIMA methods. We introduce the way of gray model and Logisticforecasting model and the principle of the two;3. Analyze the disadvantage of ARMA model and give improved method of ARMAmodel. Usually we assume that the birth rate and death rate of Leslie Matrix are constants.While they both vary when time goes on. This change is non-linear. And the time series ofbirth rate are non-stationary series, so we can’t use ARMA method directly. Then we improveARMA method to fit non-stationary series to solve this problem;4. We design a model combined improved ARMA model and Leslie Matrix. Give the data flow of this combination. Firstly, we forecast the birth rate using improved ARMA method.Secondly, we predict the death rate using ARMA method. Thirdly we correct the formerLeslie Matrix using the birth rate and death rate we predicted. Then we forecast the next yearpopulation by using this modified matrix. Use this method several times we got thepopulation of the target year;5. Test the new method and tell the advantage and disadvantage of it. Give that it canwork well in long-term forecasting.We encounter the problems that the forecasting results are not much precise when we usetraditional Leslie matrix. It is caused by using rough berth rate and rough death rate. Here weuse a modified Leslie matrix which has a detailed berth rate and death rate to get a betterresult.When we deal with non stationary sequence we encounter that ARMA method only cannot predict precisely in the long run. Here we give a newly improvement of ARMA methodand make it fit the non stationary sequence. Then we use this improved time series analysismethod to forecast the birth rate and death rate of Leslie Matrix, thus it can predict thelong-term population precisely. We compare this new method with gray theory method andLogistic method and get the result that this new method out performs the other.