Identification and Estimation of SVARMA models with Independent and Non-Gaussian Inputs

TL;DR

This paper demonstrates that SVARMA models driven by independent, non-Gaussian shocks are identifiable up to permutations and scalings, and introduces a consistent maximum-likelihood estimator for these models.

Contribution

It establishes identifiability of non-Gaussian SVARMA models and proposes a new maximum-likelihood estimator with proven consistency and asymptotic normality.

Findings

Non-Gaussian shocks enable identification up to permutations and scalings.

The proposed estimator is consistent and asymptotically normal.

Identifiability conditions make traditional restrictions testable.

Abstract

This paper analyzes identifiability properties of structural vector autoregressive moving average (SVARMA) models driven by independent and non-Gaussian shocks. It is well known, that SVARMA models driven by Gaussian errors are not identified without imposing further identifying restrictions on the parameters. Even in reduced form and assuming stability and invertibility, vector autoregressive moving average models are in general not identified without requiring certain parameter matrices to be non-singular. Independence and non-Gaussianity of the shocks is used to show that they are identified up to permutations and scalings. In this way, typically imposed identifying restrictions are made testable. Furthermore, we introduce a maximum-likelihood estimator of the non-Gaussian SVARMA model which is consistent and asymptotically normally distributed.