Robust Estimation of the non-Gaussian Dimension in Structural Linear Models (2212.07263v2)

Abstract: Statistical identification of possibly non-fundamental SVARMA models requires structural errors: (i) to be an i.i.d process, (ii) to be mutually independent across components, and (iii) each of them must be non-Gaussian distributed. Hence, provided the first two requisites, it is crucial to evaluate the non-Gaussian identification condition. We address this problem by relating the non-Gaussian dimension of structural errors vector to the rank of a matrix built from the higher-order spectrum of reduced-form errors. This makes our proposal robust to the roots location of the lag polynomials, and generalizes the current procedures designed for the restricted case of a causal structural VAR model. Simulation exercises show that our procedure satisfactorily estimates the number of non-Gaussian components.