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Biometrika 2004 91(1):240-245; doi:10.1093/biomet/91.1.240
© 2004 by Biometrika Trust
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Miscellanea

Revisiting simple linear regression with autocorrelated errors

Jaechoul Lee1 and Robert Lund1

1 Department of Statistics, The University of Georgia, Athens, Georgia 30602-1952, U.S.Ajaechlee{at}stat.uga.edu lund{at}stat.uga.edu

This paper studies properties of ordinary and generalised least squares estimators in a simple linear regression with stationary autocorrelated errors.Explicit expressions for the variances of the regression parameter estimators are derived for some common time series autocorrelation structures, including a first-order autoregression and general moving averages. Applications of the results include confidence intervals and an example where the variance of the trend slope estimator does not increase with increasing autocorrelation.

Key Words: Generalised least squares; Ordinary least squares; Simple linear regression; Time series

Received October 2002. Revised August 2003


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