Identification of noncausal ARMA models of non-Gaussian processes using higher-order statistics

The problem of estimating the parameters of a stable, scalar, noncausal autoregressive moving average (ARMA) (p,q) signal model driven by an i.i.d. non-Gaussian sequence is considered. The driving noise sequence is not observed. Two methods are proposed and analyzed: one is a multistep linear method and the other is a nonlinear optimization method. Both methods exploit both the second- and third- (or higher-) order cumulants of the observed signal. The strong consistency of the two estimators is proved. The main focus is on the linear method. Extensions to include i.i.d. measurement noise (Gaussian or non-Gaussian) can be done easily