ARMA model parameter estimation based on the equivalent MA approach

Abstract

The paper investigates the relation between the parameters of an autoregressive moving average (ARMA) model and its equivalent moving average (EMA) model. On the basis of this relation, a new method is proposed for determining the ARMA model parameters from the coefficients of a finite-order EMA model. This method is a three-step approach: in the first step, a simple recursion relating the EMA model parameters and the cepstral coefficients of an ARMA process is derived to estimate the EMA model parameters; in the second step, the AR parameters are estimated by solving the linear equation set composed of EMA parameters; then, the MA parameters are obtained via simple computations using the estimated EMA and AR parameters. Simulations including both low- and high-order ARMA processes are given to demonstrate the performance of the new method. The end results are compared with the existing method in the literature over some performance criteria. It is observed from the simulations that our new algorithm produces the satisfactory and acceptable results.