Revisiting Identification and estimation in Structural VARMA Models

The basic assumption of a structural VARMA model (SVARMA) is that it is driven by a white noise whose components are uncorrelated (or independent) and are interpreted as economic shocks, called "structural" shocks. These models have to face two kinds of identification problems. The first identification problem is "static" and is due to the fact that there is an infinite number of linear transformations of a given random vector making its components uncorrelated. The second identification problem is "dynamic" and is a consequence of the fact that the SVARMA process may have a non invertible AR and/or a MA matrix polynomial but, still, has the same second order properties as a VARMA process in which both the AR and MA matrix polynomials are invertible (the fundamental representation). Moreover the standard Box-Jenkins approach automatically estimates the fundamental representation and, therefore, may lead to misspecified Impulse Response Functions. The aim of this paper is to explain that these difficulties are mainly due to the Gaussian assumption underlying the BJ approach, and that both identification challenges are solved in a non Gaussian framework. We also develop simple new parametric and semi-parametric estimation methods when there is nonfundamentalness in either the moving-average, or the autoregressive dynamics