Regression methods in the presence of heteroscedasticity and outliers

Abstract

It has been observed over the years that real life data are usually non-conforming to the classical linear regression assumptions. One of the stringent assumptions that is unlikely to hold in many applied settings is that of homoscedasticity. When homogenous variance in a normal regression model is not appropriate, invalid standard inference procedure may result from the improper estimation of standard error when the disturbance process in a regression model present heteroscedasticity. When both outliers and heteroscedasticity exist, the inflation of the scale estimate can deteriorate. This study identifies outliers under heteroscedastic errors and seeks to study the performance of four methods; ordinary least squares (OLS), weighted least squares (WLS), robust weighted least squares (RWLS) and logarithmic transformation (Log Transform) methods to estimate the parameters of the regression model in the presence of heteroscedasticity and outliers. Real life data obtained from the Central Bank of Nigeria Bulletin and Monte Carlo simulation were carried out to investigate the performances of these four estimators. The results obtained show that the transformed logarithmic model proved to be the best estimator with minimum standard error followed by the robust weighted least squares. The performance of OLS is the least in this order