ARMA Model Parameter Optimized Estimate Method

The ARMA model is the most basic sequential method and the practical application of the most comprehensive time series model. It expands and develops in the linear regression model foundation. The ARMA model not only may promulgate dynamic data´s structure and the rule, will forecast its future value, moreover may also from the various research system´s related characteristic, the ARMA model´s parameter estimation will be studied in this model process, it is an important link, it will be a nonlinear optimization process. This article presents an ARMA model parameter estimation method, this approach uses the nonlinear least squares method which is a combination of Gauss-Newton method, and using a genetic algorithm with BFGS symmetric positive definite matrix to approximate Hesse matrix inverse, to accelerate the convergence of computing and to improve the accuracy of the estimated model parameters. Has carried on the parameter estimation and the forecast using this algorithm to GDP index series, obtained the satisfactory result. The experiment´s result had indicated that this method had the good accuracy in the parameter estimation aspect and the forecast performance.