On estimating noncausal nonminimum phase ARMA models of non-Gaussian processes

The authors address the problem of estimating the parameters of non-Gaussian ARMA (autoregressive moving-average) processes using only the cumulants of the noisy observation. The measurement noise is allowed to be colored Gaussian or independent and identically non-Gaussian distributed. The ARMA model is not restricted to be causal or minimum phase and may even contain all-pass factors. The unique parameter estimates of both the MA and AR parts are obtained by linear equations. The structure of the proposed algorithm facilitates asymptotic performance evaluation of the parameter estimators and model order selection using cumulant statistics. The method is computationally simple and can be viewed as the least-squares solution to a quadratic model fitting of a sampled cumulant sequence. Identifiability issues are addressed. Simulations are presented to illustrate the proposed algorithm