Fitting MA models to linear non-Gaussian random fields using higher-order cumulants

A general (possibly nonminimum phase and/or asymmetric noncausal) two dimensional (2-D) moving average (MA) model driven by a zero-mean i.i.d. 2-D sequence is considered. The input sequence is not observed. The signal observations may be noisy. We consider the problems of model order determination and model parameter estimation using the higher-order (third- or fourth-order, for example) cumulants of the 2-D signal. Second-order statistics of the data can consistently identify only a smaller class of MA models. Consistency of the proposed approaches is established and a simulation example is presented.