Robust Estimation of the non-Gaussian Dimension in Structural Linear Models

TL;DR

This paper introduces a robust method to determine the number of non-Gaussian components in structural errors of linear models, crucial for identifying non-fundamental SVARMA models, by linking it to the rank of a matrix derived from higher-order spectra.

Contribution

It proposes a new approach that relates the non-Gaussian dimension to the rank of a spectrum-based matrix, generalizing existing methods and improving robustness to model roots.

Findings

Accurately estimates the number of non-Gaussian components

Robust to roots location of lag polynomials

Effective in simulation studies

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.