On parameter identifiability of multidimensional non-Gaussian ARMA models using cumulant matching

Abstract

A general (possibly asymmetric noncausal and/or nonminimum phase) two-dimensional autoregressive moving average random field model driven by an i.i.d. two-dimensional (2D) non-Gaussian sequence is considered. We address the problem of parameter identifiability of the model parameters given the higher-order (third- or fourth-order, for example) cumulants of the 2D signal on a finite set of lags. The signal observations may be noisy. A key result is the parameter identifiability of 2D MA models. Using the MA parameter identifiability results, the parameter identifiability of AR and ARMA models follows immediately via a novel approach.<>