We analyze vector autoregressive processes using the matrix valued characteristic
polynomial. The purpose of this article is to give a survey of the mathematical results on …

We develop versions of the Granger–Johansen representation theorems for I (1) and I (2)
vector autoregressive processes that apply to processes taking values in an arbitrary …

A generalization of the Granger and the Johansen Representation Theorems valid for any
(possibly fractional) order of integration is presented. This Representation Theorem is based …

Almost all economic activities in modern societies are scattered through space and time.
Transport processes, as a consequence, pervade everyday life and they have deep impact …

We extend the representation theory of the autoregressive model in the fractional lag
operator of Johansen (2008, Econometric Theory 24, 651–676). A recursive algorithm for the …

Time series econometrics is centred around the representation theorems from which one
can establish the integration and cointegration characteristics of the solutions for the vector …

This note presents insights on the Jordan structure of a matrix which are derived from an
extension of the I (1) and I (2) conditions in Johansen (1996). It is first observed that these …

We show that the order of integration of a vector autoregressive process is equal to the
difference between the multiplicity of the unit root in the characteristic equation and the …

In a variety of applications, the problem comes up of describing the principal part of the
inverse of a holomorphic operator at an eigenvalue in terms of left and right root functions …

Johansen derived the asymptotic theory for his cointegration rank test statisic for a vector
autoregression where the parameters are restricted so the process is integrated of order …