Identification and estimation of Structural VARMA models using higher order dynamics

TL;DR

This paper introduces a novel method for identifying and estimating non-Gaussian SVARMA models by leveraging higher order moments and spectral density arrays, enabling more accurate structural analysis.

Contribution

It develops a frequency domain criterion for identifying non-fundamental SVARMA models using higher order cumulants, extending univariate analysis to multivariate cases.

Findings

Successful identification of model roots using higher order cumulants

Development of asymptotically normal and efficient estimators

Validation through simulations and real data analysis

Abstract

We use information from higher order moments to achieve identification of non-Gaussian structural vector autoregressive moving average (SVARMA) models, possibly non-fundamental or non-causal, through a frequency domain criterion based on a new representation of the higher order spectral density arrays of vector linear processes. This allows to identify the location of the roots of the determinantal lag matrix polynomials based on higher order cumulants dynamics and to identify the rotation of the model errors leading to the structural shocks up to sign and permutation. We describe sufficient conditions for global and local parameter identification that rely on simple rank assumptions on the linear dynamics and on finite order serial and component independence conditions for the structural innovations. We generalize previous univariate analysis to develop asymptotically normal and efficient estimates exploiting second and non-Gaussian higher order dynamics given a particular structural shocks ordering without assumptions on causality or invertibility. Bootstrap approximations to finite sample distributions and the properties of numerical methods are explored with real and simulated data.