Companion form representation of cointegrating VARs

Abstract

In this paper the issues deriving from the companion form representation of a cointegrating Vector Autoregressive system are analysed. Spectral decomposition of the companion matrix makes it possible to derive several results (including the Granger representation theorem) in a unified framework; notably, the coefficient matrices of the VMA representation are represented in such a way that long- and short-run features of the model are clearly divided. Moreover, the method proposed lends itself quite naturally to software implementations that could improve cointegrated VAR-related algorithms by avoiding recursive formulae.