Some results on the Glejser and Koenker tests for heteroskedasticity

The Glejser and Koenker (Studentized Lagrange multiplier) tests for heteroskedasticity are considered. Asymptotic theory and Monte Carlo experiments are used to investigate the effects of nonnormality under null and alternative hypotheses, and also the consequences of using an incorrect alternative. A method for using test outcomes to select models of heteroskedasticity is critically examined. Glejserʹs test is not, in general, asymptotically valid under asymmetric disturbances. Koenkerʹs test is asymptotically valid under asymmetric and other nonnormal disturbances, but has estimated finite-sample significance levels that are sometimes sensitive to skewness. An adjusted version of Koenkerʹs statistic is discussed.