Social and Behavioral Sciences Commons^™

Asymptotic Equivalence Of Ols And Gls In Regressions With Integrated Regressors, Peter C.B. Phillips, Joon Y. Park

Cowles Foundation Discussion Papers

In the multiple regression model y t = x’ t β + u t where { u t } is stationary and x t 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 …