Identification and Estimation in Non-Fundamental Structural VARMA Models

The basic assumption of a structural VARMA model (SVARMA) is that it is driven by a white noise whose components are independent and can be interpreted as economic shocks, called “structural” shocks. When the errors are Gaussian, independence is equivalent to noncorrelation and these models face two kinds of identi?cation issues. The ?rst identi?cation problem is “static” and is due to the fact that there is an in?nite number of linear transformations of a given random vector making its components uncorrelated. The second identi?cation problem is “dynamic” and is a consequence of the fact that the SVARMA process may have a non invertible AR and/or 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 [Box and Jenkins (1970)] automatically estimates the fundamental representation and, therefore, may lead to misspeci?ed Impulse Response Functions. The aim of this paper is to explain that these dif?culties are mainly due to the Gaussian assumption, and that both identi?cation challenges are solved in a non-Gaussian framework. We develop new simple parametric and semi-parametric estimation methods when there is non-fundamentalness in the moving average dynamics. The functioning and performances of these methods are illustrated by applications conducted on both simulated and real data.