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This note shows that the ordinary least squares estimator of a first-order autoregressive model is always more efficient relative to the Cochrane-Orcutt estimator if the autocorrelation process has a finite past than if its past is infinite. This result cast doubt on the usual suggestion that it might be better to delete the initial observation rather than weight it if the autocorrelation process has a finite past.

A Note on the Relative Efficiency of the Cochrane-Orcutt and OLS Estimators when the Autocorrelation Process has a Finite Past