The Algebraic Framework of Unit-Root Econometrics

Abstract

Time series econometrics is centred around the representation theorems from which one can evict the integration and cointegration characteristics of the solutions for the vector autoregressive (VAR) models.

Such theorems, along the path established by Engle and Granger and by Johansen and his school, have promoted the parallel development of an “ad hot” analytical implement — although not always fully settled.

The present chapter, by reworking and expanding some recent contributions due to Faliva and Zoia, provides in an organic fashion an algebraic setting based upon several interesting results on inversion by parts and on Laurent series expansion for the reciprocal of a matrix polynomial in a deleted neighbourhood of a unitary root. Rigorous and efficient, such a technique allows for a quick and new reformulation of the representation theorems as it will become clear in Chapter 3.