Dynamic factor and VARMA models: equivalent representations, dimension reduction and nonlinear matrix equations

TL;DR

This paper demonstrates the equivalence between dynamic factor models with VAR$(p)$ factors and VARMA$(p,p)$ models, introduces reduced-rank structures, and links parameter estimation to nonlinear matrix equations.

Contribution

It establishes the theoretical equivalence between dynamic factor and VARMA models, and develops methods for parameter computation using nonlinear matrix equations.

Findings

VAR and VMA components have reduced-rank structures.

VMA parameters can be numerically computed from original model parameters.

Connections to nonlinear matrix equations are established.

Abstract

A dynamic factor model with factor series following a VAR$(p)$ model is shown to have a VARMA$(p,p)$ model representation. Reduced-rank structures are identified for the VAR and VMA components of the resulting VARMA model. It is also shown how the VMA component parameters can be computed numerically from the original model parameters via the innovations algorithm, and connections of this approach to non-linear matrix equations are made. Some VAR models related to the resulting VARMA model are also discussed.