A general inversion theorem for cointegration
A generalization of the Granger and the Johansen Representation
Theorems valid for any (possibly fractional) order of integration is pre-
sented. This Representation Theorem is based on inversion results that
characterize the order of the pole and the coefficients of the Laurent series
representation of the inverse of a matrix function around a singular point.
Explicit expressions of the matrix coefficients of the (polynomial) cointe-
grating relations, of the Common Trends and of the Triangular representa-
tions are provided, either starting from the Moving Average or the Auto
Regressive form. This contribution unifies different approaches in the litera-
ture and extends them to an arbitrary order of integration. The role of
deterministic terms is discussed in detail.