Bookcover of The Efficiency of OLS in the Presence of Auto- correlated Errors
Booktitle:

# The Efficiency of OLS in the Presence of Auto- correlated Errors

## The Efficiency of OLS in the Presence of Auto- correlated Errors

VDM Verlag Dr. Müller (2008-10-02 )

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ISBN-13:

### 978-3-639-08690-4

ISBN-10:
3639086902
EAN:
9783639086904
Book language:
English
Blurb/Shorttext:
It is known that the ordinary least squares (OLS) estimates in the regression model are efficient when the errors have mean zero, constant variance and are uncorrelated. In time series, it is often the errors are correlated. It is known that OLS may not be optimal in this context. We have proved that the relative efficiency of the variance of the generalized least squares (GLS) to that of OLS is invariant to scaling and shifting of the design vectors. We have derived explicit formulae for the relative efficiencies of the GLS to that of OLS in some important special cases. We consider both linear and quadratic design vectors in the presence of AR(1) errors and show some asymptotic properties of the estimators. Additionally, using computer simulations, we consider the robustness of various estimators, including estimated GLS. We found that if the error structure is autoregressive and the dependent variable is nonstochastic and linear or quadratic, the OLS performs nearly as well as its competitors. For other forms of the dependent variable, we have developed rules of thumb to guide practitioners in their choice of estimators.
Publishing house:
VDM Verlag Dr. Müller
Website:
http://www.vdm-verlag.de
By (author) :
Safi Samir
Number of pages:
164
Published at:
2008-10-02
Stock:
Available
Category:
Mathematics
Price:
68.00 €
Keywords:
efficiency, correlated, Disturbances, Estimators, OLS, GLS, time series, regression, Autoregressive