The small-sample properties of some preliminary test estimators in a linear model with autocorrelated errors

Abstract A Monte Carlo study is used to examine the finite-sample relative efficiency of a number of estimators (including pre-test estimators), and the accuracy of asymptotic confidence intervals derived from them, for a linear model with AR(1) or MA(1) errors. The bias of the ML estimator of the AR(1) parameter, and the frequency of ML estimates equal to ±1 for the MA(1) parameter, have a large bearing on the properties of the estimators of the regression coefficient. The traditional OLS-AR pre-test estimator compares relatively favorably, even under an MA error specification. However, the confidence intervals associated with positive autoregressive errors and a trended explanatory variable can be quite inaccurate.

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