  This article deals with parameterisation, identifiability, and maximum
likelihood (ML) estimation of possibly non-invertible structural vector
autoregressive moving average (SVARMA) models driven by independent and
non-Gaussian shocks. In contrast to previous literature, the novel
representation of the MA polynomial matrix using 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.
Typically imposed identifying restrictions on the shock transmission matrix as
well as on the determinantal root location are made testable. Furthermore, we
provide low level conditions for asymptotic normality of the ML estimator and
analytic expressions for the score and the information matrix. As application,
we estimate the Blanchard and Quah model and show that our method provides
further insights regarding non-invertibility using a standard macroeconometric
model. These and further analyses are implemented in a well documented
R-package.
