Before revision:  We introduce a new parameterisation of the MA polynomial matrix based on the Wiener-Hopf factorisation (WHF) and show that the model is identified in this parametrisation for a generic set in the parameter space (when certain just-identifying restrictions are imposed). When the SVARMA model is driven by Gaussian errors, neither the static shock transmission matrix, nor the location of the determinantal zeros of the MA polynomial matrix can be identified without imposing further identifying restrictions on the parameters. We characterise the classes of observational equivalence with respect to second moment information at different stages of the modelling process. Subsequently, cross-sectional and temporal independence and non-Gaussianity of the shocks is used to solve these identifiability problems and identify the true root location of the MA polynomial matrix as well as the static shock transmission matrix (up to permutation and scaling) .
After revision:  We introduce a new parameterisation of the MA polynomial matrix based on the Wiener-Hopf factorisation (WHF) focuses on the multivariate nature of the model, generates insights into its structure, and uses this structure for devising optimisation algorithms. In particular, it allows to parameterise the location of determinantal zeros inside and outside the unit circle, and it allows for MA zeros at zero, which can be interpreted as informational delays. This is highly relevant for data-driven evaluation of Dynamic Stochastic General Equilibrium (DSGE) models .