Estimation in least absolute value regression with autocorrelated errors

Abstract

Least absolute value (LAV) regression provides a robust alternative to least squares, particularly when the disturbances follow distributions that are nonnormal and subject to outliers. The performance of the least squares estimator when the errors are autocorrelated has been studied extensively; the performance of the least absolute value estimator in the presence of serial correlation is less well established. In this work, we study the performance of various LAV-based estimation techniques for simple time series regression when the errors are autocorrelated and compare the least absolute value estimators to their least squares-based counterparts. Monte Carlo simulation methods are used to compare the small sample performances of the different estimators. Our results indicate that, for the small sample situations considered, a Prais-Winsten-type least absolute value estimator, in which all of the available observations are used, is preferable to a Cochrane-Orcutt-type least absolute value estimator, in which the first observation is omitted.

Keywords:

• Robust regression
• L ₁ regression
• Least absolute deviations
• Serial correlation
• Cochrane-Orcutt correction
• Prais-Winsten correction