The frisch-waugh theorem and generalized least squares |
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Authors: | Denzil G Fiebig Robert Bartels |
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Institution: | 1. Department of Econometrics , University of Sydney , Sydney, NSW, 2006, Australia;2. Department of Statistics , University of Dortmund , Dortmund, D-44227, Germany |
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Abstract: | We discuss the standard linear regression model with nonspherical disturbances, where some regressors are annihilated by considering only the residuals from an auxiliary regression, and where, analogous to the Frisch-Waugh procedure, the original GLS procedure is applied to the transformed data. We call this procedure pseudo-GLS and give conditions for pseudo-GL5 to be equal to genuine GLS. We also show via examples that these conditions are often violated in empirical applications, and that the Frisch-Waugh Theorem still “works” with nonspherical disturbances if efficient estimation is applied to both the original and the transformed data. |
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Keywords: | ADF tests Unit roots Asymptotics Linear process Autoregressive approximation |
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