Identification and estimation of Structural VARMA models using higher order dynamics

We use information from higher order moments to achieve identification of non-Gaussian structural vector autoregressive moving average (SVARMA) models, possibly nonfundamental or noncausal, through a frequency domain criterion based on spectral densities. This allows us identify the location roots determinantal lag matrix polynomials and rotation model errors leading shocks up sign permutation. describe sufficient conditions for global local parameter that rely simple rank assumptions linear dynamics finite serial component independence innovations. generalize previous univariate analysis develop asymptotically normal efficient estimates exploiting second cumulant given particular ordering without causality invertibility. Finite sample properties are explored with real simulated data.