We propose a new class of estimators for semiparametric VARMA models with unspecified innovation density. Our estimators are based on the measure transportation-based  concepts of multivariate center-outward  ranks and signs. Root-n consistency and asymptotic normality are obtained under a broad class of innovation densities including, e.g.,  multimodal mixtures of Gaussians. Simulations establish the impressive performances of the resulting R-estimators, which quite significantly outperform, under non-Gaussian and non-elliptical innovation densities, the routinely-applied Gaussian quasi-likelihood  method.

Based on joint work with Davide La Vecchia (University of Geneva) and Hang Liu (Lancaster University)