Parameter identifiability of multichannel ARMA models of linear non-Gaussian signals via cumulant matching

The problem of estimating the parameters of a vector, stationary, ARMA(p, q) signal model driven by an i.i.d. vector non-Gaussian sequence is considered. The focus of this correspondence is the problem of parameter identifiability of multichannel ARMA models given the higher order cumulants of the signal on a finite set of lags. We specify the finite lag set for general ARMA(p, q) models. Our approach is to first derive the basic results via a diagonal canonical form and then to extend the parameter identifiability results to other (more parsimonious) canonical forms.