Maximum Likelihood Estimation of Cointegrated Systems with Higher Order Integrated Variables and Asymptotic Equivalence with Generalised Least Squares

This paper is concerned with the estimation of cointegrated systems with integrated variables of order greater than 1. Unlike the case of I(1) variables, there are various possibilities of cointegration in the higher order case, which were conveniently formulated in a triangular representation and estimated by Ordinary Least Squares (OLS) and Generalised Least Squares (GLS) by STock and Watson (1993). Starting from this triangular representation, we derive an error correction model that already incroporates the diffrent cointegration restrictions and apply maximum likelihood to estimate the parameters.