Parameter estimation for noncausal ARMA models of non-Gaussian signals via cumulant matching

We consider the problem of estimating the parameters of a stable (stationary), scalar ARMA(p,q) signal model driven by an i.i.d. non-Gaussian sequence. The driving noise sequence is not observed. The signal is allowed to be nonminimum phase and/or noncausal (i.e., poles may lie both inside as well as outside the unit circle). We address the problem of parameter identifiability given the higher order cumulants of the signal on a finite set of lags. The sufficient set of lags required to achieve parameter identifiability is the smallest to date. The sufficient conditions for parameter identifiability are also the least restrictive to date. We also propose a frequency-domain approach for time-domain, nonlinear optimization of a quadratic cumulant matching criterion. Illustrative computer simulation results are presented