ARMA model identification from noisy observations based on a two-step errors-in-variables approach

Abstract

This paper proposes a new method for identifying ARMA models in the presence of additive white noise. The method operates with two main steps. First, the noisy ARMA model is approximated by the sum of an high-order AR model with an additive white noise. The parameters of the high-order AR model as well as the driving noise and the additive noise variances are estimated by using an errors-in-variables approach. Second, the coefficients of the ARMA model are extracted from those of the AR model previously identified by means of existing techniques. In particular, three different methods are considered and compared for solving the second step. The effectiveness of the described identification procedure has been tested by Monte Carlo simulations and compared with a prediction error method.