The Two Methods Of Conjugate Gradient Parameters Estimation Of Arma Model And The Application Of The Arimax Model

As one of the branches of statistic, time series is the objective records of the history behavior of the system studied. It contains the system structure and its operation rule and 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 optimization algorithm methods as follows: Newton method, steepest descent method and conjugate gradient method.This paper studies the two optimization algorithm methods of parameters estimation of ARMA model and the application of the ARIMAX model.First of all, we mainly show the purposes of time series analysis, the development history and current state of time series analysis, and analyze the development foreground of time series analysis and expound the development history of the conjugate gradient method.Secondly, we introduce the parameter estimation methods for ARMA model and model test. This chapter introduces Newton method, steepest descent method and conjugate gradient method.Thirdly, we make up a new kind of conjugate gradient method which contains two parameters and the application of it in the non-linear time series ARMA model. In this chapter, the ARMA model parameter estimation is transformed into a no-constrained optimization problem, the traditional conjugate gradient method is improved appropriately and we get a new algorithm. So we can using the algorithm to estimate the parameters in ARMA model.Fourthly, we make up another new kind of conjugate gradient method which contains three parameters and the application of it in the non-linear time series ARMA model. In this chapter, we use the test functions to verify the new algorithm and results show that the effect is good.Lastly, we give the diversity time series model——ARIMAX model to solve the problem of forecast analysis of economic non-stationary time series. For the Shanghai index in 2003.9—2007.10, we mode and predict it with SAS software.