Asymptotic Equivalence of OLS (GLS) and Maximum Likelihood using Cointegrated Systems with Higher Order Integrated Variables

Résumé

Abstract
This paper is concerned with the estimation of cointegrated systems with integrated variables of order greater than 1. Unlike in the case of order 1 cointegrated variables I(1), 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 Generalized Least Squares (GLS) by Stock and Watson (1993). Starting from this triangular representation, we derive an error correction
model that already incorporates the different cointegration restrictions and apply maximum likelihood to estimate the parameters. Our approach is compared with that of Johansen (1995) and Kitamura (1995). Asymptotic properties of our maximum likelihood (ML) estimators are derived. Further, it is shown that as far as the coefficients of integrated variables
are concerned, our ML estimators are asymptotically equivalent to the OLS/GLS estimators of Stock and Watson (1993).