On estimating non-causal ARMA non-Gaussian processes

The authors consider the identification of non-Gaussian ARMA (autoregressive moving average) processes using columnant statistics of noisy observations. The measurement noise is allowed to be colored Gaussian or independent and identically non-Gaussian distributed. It is not necessary to know whether the ARMA model is causal or noncausal, minimum phase or nonminimum phase. The unique parameter estimates of both the MA and AR parts are obtained via linear equations. The structure of the proposed algorithm facilitates asymptotic performance evaluation of the parameters estimators and model order selection using cumulant statistics. It is concluded that the method is computationally simple and can be viewed as the mean-square optimal model fitting of a sampled cumulant sequence. Simulations are presented to illustrate the proposed algorithm.