Granger's Representation Theorem and Multicointegration

We consider multicointegration in the sense of Granger and Lee (1990), that is, the cumulated equilibrium error cointegrates with the process itself. It is shown, that if the process is given by the cointegrated VAR model for I(1) variables, then multicointegration cannot occur. If, however, the cumulated process satisfies an I(2) model then multicointegration may occur. Finally conditions are given on the moving average representation for the process to exhibit multicointegration. This result generalizes the analysis of Granger and Lee.