Identifiability and estimation of possibly non-invertible SVARMA Models: The normalised canonical WHF parametrisation

Abstract

This article focuses on the parametrisation, identifiability, and (quasi-) maximum likelihood (QML) estimation of possibly non-invertible structural vector autoregressive moving average (SVARMA) models. SVAR models are routinely adopted due to their well-known implementation strategy. However, for various economic and statistical reasons, multivariate SVARMA settings are often more suitable. These settings introduce complexity in the analysis, primarily due to the presence of the moving average (MA) polynomial. We propose a novel representation of the MA polynomial matrix using the Wiener–Hopf factorization (WHF). A significant advantage of the WHF is its ability to handle possible non-invertibility and thus models with informational asymmetry between economic agents and outside observers. Since solutions of Dynamic Stochastic General Equilibrium (DSGE) models often involve this informational asymmetry, SVARMA models in WHF parametrisation can be considered data-driven alternatives to DSGE models and used for their evaluation. Furthermore, we provide low-level conditions for the asymptotic normality of the (Q)ML estimator and analytic expressions for the score and information matrix. As application, we estimate the Blanchard and Quah model, and compare our results and implied impulse response function with the ones in the SVAR model by Blanchard and Quah and a non-invertible SVARMA model by Gouriéroux and co-authors. Importantly, we have implemented this novel method in a well-documented R-package, making it readily accessible for researchers and practitioners.