On the State–space Realization of Vector Autoregressive Structures: An Assessment

Abstract

This study explores the interconnection between vector autoregressive (VAR) structures and state-space models and results in a compact framework for the representation of multivariate time-series, as well as the estimation of structural information. The corresponding methodology that is developed, applies the fact that every VAR process of order n may be described by an equivalent (non-unique) VAR model of first order, which is identical to a state-space realization. The latter uncovers many "hidden" information of the initial model, it is more easy to manipulate and maintains significant second moments' information that can be reflected back to the original structure with no effort. The performance of the proposed framework is validated using vector time-series signatures from a structural system with two degrees of freedom, which retains a pair of closely spaced vibration modes and has been reported in the relevant literature.