Identification and Estimation in Non-Fundamental Structural VARMA Models

Abstract

<jats:title>Abstract</jats:title> <jats:p>The basic assumption of a structural vector autoregressive moving average (SVARMA) model is that it is driven by a white noise whose components are uncorrelated or independent and can be interpreted as economic shocks, called “structural” shocks. When the errors are Gaussian, independence is equivalent to non-correlation and these models face two identification issues. The first identification problem is “static” and is due to the fact that there is an infinite number of linear transformations of a given random vector making its components uncorrelated. The second identification problem is “dynamic” and is a consequence of the fact that, even if a SVARMA admits a non-invertible moving average (MA) matrix polynomial, it may feature the same second-order dynamic properties as a VARMA process in which the MA matrix polynomials are invertible (the fundamental representation). The aim of this article is to explain that these difficulties are mainly due to the Gaussian assumption, and that both identification challenges are solved in a non-Gaussian framework if the structural shocks are assumed to be instantaneously and serially independent. We develop new parametric and semi-parametric estimation methods that accommodate non-fundamentalness in the MA dynamics. The functioning and performances of these methods are illustrated by applications conducted on both simulated and real data.</jats:p>

Statistical inference for independent component analysis: Application to structural VAR models

“…[see e.g. Gourieroux, Monfort (2014), Gourieroux, Jasiak (2015), for the estimation of such parameters by covariance estimators].…”

“…In particular it can be used to identify independent shocks in a structural vector autoregressive (SVAR) model [see e.g. Chen, Choi, Escanciano (2012), Moneta et al (2013), Gourieroux, Monfort (2014)]. In this case the explanatory variables X t are lagged endogenous variables and the model of interest is:…”

Estimation and forecasting in vector autoregressive moving average models for rich datasets

“…Finally, it is important to note that the VARMA representation in (1) is not a structural VARMA (SVARMA) model in its classical definition (see Gourieroux and Monfort (2015)), because (1) is not necessarily driven by independent (or uncorrelated) shocks. To construct impulse response functions, which depend on the structural shocks, additional identification restrictions to the ones required for uniqueness are necessary.…”

Do Rising Top Incomes Spur Economic Growth? Evidence From OECD Countries Based on a Novel Identification Strategy

“…In this paper, we take advantage of recent contributions to identification in structural‐vector autoregressive (SVAR) models. As shown by Lanne et al ., (), Moneta et al ., (), and Gouriéroux and Monfort (), the traditional identification problem of distinguishing between rival causation patterns—for example, Cholesky factors (Sims, ) or long‐run relations (Blanchard and Quah, )—can be resolved in a data‐driven manner in non‐Gaussian systems. Specifically, the detection of independent orthogonalized shocks in non‐Gaussian systems provides external information which allows the testing of otherwise just‐identifying structural assumptions.…”