Econometrica: Jan 1979, Volume 47, Issue 1

Efficiency of Least-Squares Estimation of Linear Trend when Residuals Are Autocorrelated

https://doi.org/0012-9682(197901)47:1<115:EOLEOL>2.0.CO;2-3
p. 115-128

John S. Chipman

In the regression model y"t = @a + @bt + @e"t is found that when the residuals @e"t follow a first-order stationary Markoff process with zero mean and autocorrelation coefficient @r, - 1 < @r < 1, the greatest lower bound for the efficiency of the least-squares estimator of @b (relative to the Gauss-Markoff estimator) over the interval 0 @? @r < 1 is .753763. This compares with a greatest lower bound of .535898 for the relative efficiency of the Cochrane-Orcutt estimator of @b.
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