Errors-in-variables identification of noisy moving average models

In this paper, we propose to address the moving average (MA) parameters estimation issue based only on noisy observations and without any knowledge on the variance of the additive stationary white Gaussian measurement noise. For this purpose, the MA process is approximated by a high-order AR process and its parameters are estimated by using an errors-in-variables (EIV) approach, which also makes it possible to derive the variances of both the driving process and the additive white noise. The method is based on the Frisch scheme. One of the main difficulties in this case is to evaluate the minimal AR-process order that must be considered to have a 'good' approximation of the MA process. To this end, we propose a way based on K-means method. Simulation results of the proposed method are presented and compared to existing MA-parameter estimation approaches.