Using the Prais-Winsten correction and adding a lagged variable provides improved estimates (smaller MSE) in least absolute value (LAV) regression when moderate to high levels of autocorrelation are present. When comparing empirical levels of significance for hypothesis tests, adding a lagged variable outperforms other approaches but has a relative high empirical level of significance.
Dielman, Terry E.
"Estimation and Hypothesis Testing in LAV Regression with Autocorrelated Errors: Is Correction for Autocorrelation Helpful?,"
Journal of Modern Applied Statistical Methods: Vol. 10
, Article 13.
Available at: http://digitalcommons.wayne.edu/jmasm/vol10/iss2/13