Identifiability and Estimation of Possibly Non-Invertible SVARMA Models: A New Parametrisation

TL;DR

This paper introduces a new parametrisation and estimation method for possibly non-invertible SVARMA models using Wiener-Hopf factorisation, enabling better analysis of model structure and non-invertibility in macroeconomic data.

Contribution

It proposes a novel multivariate parametrisation of SVARMA models with Wiener-Hopf factorisation, facilitating identifiability, estimation, and analysis of non-invertibility.

Findings

New parametrisation of MA polynomial matrix using Wiener-Hopf factorisation

Application to macroeconomic DSGE models and insights into non-invertibility

Implementation of estimation method in an R-package

Abstract

This article deals with parameterisation, identifiability, and maximum likelihood (ML) estimation of possibly non-invertible structural vector autoregressive moving average (SVARMA) models driven by independent and non-Gaussian shocks. In contrast to previous literature, the novel representation of the MA polynomial matrix using the Wiener-Hopf factorisation (WHF) focuses on the multivariate nature of the model, generates insights into its structure, and uses this structure for devising optimisation algorithms. In particular, it allows to parameterise the location of determinantal zeros inside and outside the unit circle, and it allows for MA zeros at zero, which can be interpreted as informational delays. This is highly relevant for data-driven evaluation of Dynamic Stochastic General Equilibrium (DSGE) models. Typically imposed identifying restrictions on the shock transmission matrix as well as on the determinantal root location are made testable. Furthermore, we provide low level conditions for asymptotic normality of the ML estimator and analytic expressions for the score and the information matrix. As application, we estimate the Blanchard and Quah model and show that our method provides further insights regarding non-invertibility using a standard macroeconometric model. These and further analyses are implemented in a well documented R-package.