Autocorrelation Pre-Testing in Linear Models with AR(1) Errors

Abstract

The first part of the paper gives an overview of the recent literature on autocorrelation pre-testing in linear models. Pre-testing is found to be preferable to pure OLS and to outperform the procedures of always correcting for autocorrelation. The Durbin pre-test estimator, applying the Durbin-Watson test of autocorrelation, compares favorably with its alternative pre-test estimators. However, especially in the case of positive autoregressive errors and a trended explanatory variable the estimated risk of the Durbin estimator increases substantially beyond values of 0.6 for the autocorrelation parameter. Moreover, the confidence intervals can be quite inaccurate. In the second part of the paper the problem how to assess the reliability of coefficient estimates of data-instigated models is investigated. Some aspects of the distribution of the pre-test estimator (applying the Durbin-Watson test of autocorrelation and the Durbin estimator in the case the hypothesis of uncorrelated disturbances is rejected) are approximated by the bootstrap technique. The main finding is that the unbiasedness of the pre-test estimator of the regression coefficient on average also holds over the bootstrap distributions. The 90% confidence interval proportions obtained by the bootstrap technique, however, are substantially lower than in the case of the pre-test estimator. Another important result is that the Durbin estimator of the autocorrelation parameter is seriously biased downwards which has a substantial impact on the performance of the pre-test estimator.