Testing for GARCH effects: a one-sided approach

ARCH models often lie at the boundary of the parameter space under conditional homoskedasticity, which invalidates the usual χ2 distribution of LR and Wald tests. Although LM tests are not affected, the one-sided nature of the alternative hypothesis should result in more powerful tests. We propose a simple one-sided version of the LM test, which is closely related to the Kuhn–Tucker multiplier test. We also present critical values for LR, Wald and one-sided LM tests. The results of a Monte Carlo comparison suggest that one-sided tests are indeed more powerful than their two-sided counterparts.