Estimating the autocorrelated error model with trended data

by Rolla Edward Park, Bridger M. Mitchell

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The time-series model with first-order autocorrelation arises in a wide variety of econometric applications. This report compares the relative efficiencies of seven estimators of the structural coefficients beta in samples of 20 and 50 observations and assesses the performance of the conventionally used variance statistics for testing hypotheses when the independent variables contain a trend. The estimators compared are (1) ordinary least squares (OLS), (2) Cochrane-Orcutt (C-O), (3) feasible C-O (using the estimated autocorrelation coefficient rho), (4) generalized least squares (GLS), (5) feasible GLS, (6) first difference (FD), and (7) FD with an estimated intercept. As a practical guide, it is recommended (1) not to use the C-O estimator, (2) to use feasible GLS for important problems, (3) to use FD only when it is known that high autocorrelation is present, and (4) to distrust [t]-statistics and apply substantially higher confidence levels for testing hypotheses.

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