| As one of the branches of statistic, time series analysis focus on the variation characters and trend of discrete ordered data series mainly. For a long time, time series analysis have been applying in many fields successfully, such as economics, finance, management, chronometer, aerograph, physical geography, oceanography, biology, mechanics, electronic engineering etc.It displays the developing transformation about the researched object during a interval time and finds the character trend through the analyzing the old measured data, so we can predict the object state in future in order to make decision. Therefore, modeling theory about time series plays the important role in data analysis field. Finding better modeling in order to make a forecast exactly, however, the estimation of parameters takes precedence of the modeling. There are three methods as follows: moment estimate, maximum likelihood estimate and least squares estimate.This paper studies the two methods of parameters estimation of ARMA model and the application of the Auto-Regressive model.First of all, we introduce the parameter estimation methods for ARMA model and model test. This chapter introduces moment estimate, maximum likelihood estimate and least squares estimate.Secondly, we introduce a kind of optimization estimation method of the non-linear time series ARMA model named the damped least square method, which combines the advantage of Newton and the rapidest descend. MATLAB program for estimating its parameters is given. Thirdly, we introduce another kind of optimization estimation method ofthe non-linear time series ARMA model named NLBFGS method, MATLAB program for estimating its parameters is given, with an example showing that the model is marked by T test. Lastly, we apply the Auto-Regressive model to analyze the value of our country from 1978 to 2005, and apply the model to forecast variables in the end, which apply MATLAB, the process of the modeling has come true.
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