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On the unique representation of non-Gaussian multivariate linear processes

In contrast to the fact that Gaussian linear processes generally have nonunique moving-average representations, non-Gaussian univariate linear processes have been shown to admit essentially unique moving-average representation, under various regularity conditions. We extend the one-dimensional result to multivariate processes. Under various conditions on the intercomponent dependence structure of the error process, we prove that for non-Gaussian multivariate linear processes the moving-average representation is essentially unique under the condition that the transfer function is of full-rank, plus other mild conditions.