Comment on Gouri\'eroux, Monfort, Renne (2019): Identification and Estimation in Non-Fundamental Structural VARMA Models

TL;DR

This paper critiques a previous work on structural VARMA models, highlighting a flaw involving complex roots and discussing the practical limitations of the proposed method for higher-dimensional cases.

Contribution

It identifies a critical flaw in the earlier methodology related to complex roots and evaluates the feasibility of the proposed approach for larger models.

Findings

Identifies a flaw in the handling of complex roots with Blaschke matrices.

Discusses the impracticality of the method for high-dimensional models.

Highlights limitations for vector moving average polynomial matrices of degree greater than one.

Abstract

This comment points out a serious flaw in the article "Gouri\'eroux, Monfort, Renne (2019): Identification and Estimation in Non-Fundamental Structural VARMA Models" with regard to mirroring complex-valued roots with Blaschke polynomial matrices. Moreover, the (non-) feasibility of the proposed method (if the handling of Blaschke transformation were not prohibitive) for cross-sectional dimensions greater than two and vector moving average (VMA) polynomial matrices of degree greater than one is discussed.