There is considerable evidence that many econometric models make use of variables which give rise to error term distributions characterized by fat-tails or infinite variance. Usually linear models are estimated by the Ordinary Least Squares (OLS) or Maximum Likelihood Estimator, (MLE) by assuming normality. When estimating linear models, where fat-tailed and serially dependent residuals appear, it is important to find robust alternatives to these estimators. This is especially true in the case of small sample estimation. An alternative to the OLS estimator is Least Absolute Error (LAE). In this Paper Least Absolute Error Estimation of Linear Regression Models with Auto Correlated errors are discussed and observed that least squares based on absolute errors are preferable over the methods, when the errors are normally distributed.