Algorithm Improvement Of Parameter Estimation For Arma Model And Application Of Sarima Model

As one of the branches of statistics, 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 common methods as follows: moment estimate, maximum likelihood estimate and least squares estimate.This paper studies an improved algorithm of parameter estimation for ARMA model and the application of SARIMA model and GARCH model in the practical problems.First of all, we give an improved algorithm of parameter estimation for the non-linear time series ARMA model. This algorithm determines initial value based on Y-W method and invertible function method, combine with the damped least square method in the optimization theory to solve parameter of the model. Thus forms the non-linear time series optimal estimation method. MATLAB is used to analyze an example and test the availability of the algorithm.Secondly, we apply the SARIMA model to analyze the social retail goods series of our country from 2001 to 2008, and apply the model to modeling and forecasting variables, which apply SAS software, the process of the modeling and forecasting has come true. The paper model and forecast the series with two kinds of SARIMA models and contrast the two results of the forecasting for the two methods of modeling.Lastly, we apply the GARCH model to model and analyze the values of a group of financial series, and get perfect results.