Misspecification and estimation effect in the Lagrange multiplier tests for heteroskedasticity
The article considers the behaviour of the Lagrange multiplier (LM) tests for conditional and unconditional heteroskedasticity. These tests are based on auxiliary equations having as dependent variable the residuals from the main equation. Some studies have found that the LM tests for conditional heteroskedasticity over-reject the true null, whereas the LM tests for unconditional heteroskedasticity have an under-rejection problem. In order to improve the empirical size of these tests, different ad hoc correcting factors have been presented in the literature. Instead we propose to implement the auxiliary equation with better quality residuals, that is, with residuals from the median regression (LAD) instead of residuals from the mean regression (OLS). We show that the use of LAD residuals does not alter the asymptotic distribution of the LM test. The Monte Carlo study finds that the tests based on LAD residuals improve upon the same test functions implemented using OLS residuals. The improvement granted by LAD has the additional advantage of avoiding the various ad hoc correcting factors defined by different authors to solve the size problems of the analyzed test functions.
conditional and unconditional heteroskedasticity median regression