Identification of possibly nonfundamental VARMA models using higher order moments

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We introduce a frequency domain criterion to identify the parameters of, possibly noncausal and/or noninvertible, vector autoregressive moving average (VARMA) models. We use information from higher order moments to achieve identification on the location of the roots of the VAR and VMA matrix polynomials for non-Gaussian vector time series possibly non-fundamental. We develop general representations of the higher order spectral density arrays of vector linear processes and describe sufficient conditions for the parameter identification that rely on both sufficiently rich (linear) dynamics and higher order dependence structure of the vector of linear innovations. These results generalize previous univariate analysis to develop more efficient estimates and relate to the predictability of Wold innovations of nonfundamental processes.