Identification of possibly nonfundamental Structural VARMA models using higher order moments

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We use information from higher order moments to achieve identification of non-Gaussian structural vector autoregressive moving average (SVARMA) models, possibly non-fundamental. We introduce a frequency domain criterion to identify the location of the roots of the lag matrix polynomials based on higher order cumulants dynamics. This information also provides identification on the rotation of the model errors leading to the structural innovations up to sign and permutation. We develop general representations of the higher order spectral density arrays of vector linear processes and describe sufficient conditions for global and local parameter identification that rely on simple rank conditions on the linear dynamics and on moment implications of the independence component assumption on the vector of structural innovations. We generalize previous univariate asymptotic analysis to develop asymptotically normal and efficient estimates exploiting second and higher order dynamics.