The Model About ARMA And Its Application

Time series analysis is an important offset of statistics, which studys the orderliness of stochastic data series with stochastic process theory and statistical methods. Time series analysis provides a suit of methods dealing with dynamic data, the most important measure of this method is to approximately depict many kinds of data by relevant mathematical models. With the analysis and investigation, we can constitutionally know the inherent structure and complex character, so we can achieve the purpose of forecasting its development trend and putting up essential control.This thesis studies ARMA model and its application, includes five chapters.In the first chapter, we mainly show the methods of time series analysis, the development history and current state of time series analysis, and analyze the development foreground of time series analysis.In the second chapter, we basically introduce the statistical character of the model about ARMA in common use.In the third chapter, we introduce the parameter estimation methods for ARMA model and model test. This chapter introduces the moment estimate,maximum likelihood estimate and least squares estimate, and mainly introduces the two-stage recursive least squares-recursive extended least squares parameter estimation method for ARMA model, viz. modified recursive extended least squares method. At last, we introduce the test for ARMA model.In the fourth chapter, we first briefly discuss the methods of forecasting for ARMA model, then we analyze a commodity's monthly sale through the Matlab software, establish the model for time series by two-stage recursive least squares-recursive extended least squares parameter estimation method, then test the feasibility of the model, and in the end forecast variables.In the fifth chapter, we analyze the parameter estimation for mixed auto regression moving average model, the estimation of parameters is easily performed via expectation maximization algorithm, and we make a simulation for the estimation at last.