CFDP 802

Asymptotic Equivalence of OLS and GLS in Regressions with Integrated Regressors


Publication Date: September 1986

Pages: 21


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.


Asymptotic efficiency, Integrated regressors, Invariance principle, Multiple regression, Vector Brownian motion

See CFP: 703