The effect of variance estimation of regression coefficients when disturbances are serially correlated in time series regression models is studied. Variance estimation enters into confidence interval estimation, hypotheses testing, spectrum estimation, and expressions for the estimated standard error of prediction. Using computer simulations, the robustness of various estimators, including Estimated Generalized Least Squares (EGLS) was considered. The estimates of variance of the coefficient estimators produced by computer packages were considered. Models were generated with a second order auto-correlated error structure, considering the robustness of estimators based upon misspecified order. Ordinary Least Squares (OLS) (order zero) estimates outperformed first order EGLS. A full comparison of order zero and four estimators indicate that over specification is preferable to under specification.