Asymptotic Equivalence of OLS and GLS in Regressions with Integrated Regressors

In the multiple regression model yt = x’tβ + ut where {ut} is stationary and xt is an integrated m-vector process it is shown that the asymptotic distributions of the ordinary least squares (OLS) and generalized least squares (GLS) estimators of β are identical. This generalizes a recent result obtained by Kramer (1986) for simple two variate regression. Our approach makes use of a multivariate invariance principle and yields explicit representations of the asymptotic distributions in terms of fuctionals of vector Brownian motion. Some useful assumption results for hypothesis tests in the model are also provided.