If I didn't misunderstand the literature, the predominant approach to test for autoregressive conditional heteroscedasticity in (G)ARCH models is to apply the ARCH LM test of Engle or the Ljung-Box test on the squared (non-standardized) residuals.
Alternatively, the Li-Mak test can be applied on the squared standardized residuals. Why should this test be preferred over the others? Is it because we assume for GARCH models that the standardized residuals are iid? If yes, please elaborate.
Best Answer
ARCH-LM and Ljung-Box (LB) tests are to be applied on raw data* or on residuals* of a model that does not allow for ARCH patterns. Meanwhile, Li-Mak test is to be applied on standardized residuals of a model that does allow for ARCH patterns, e.g. a GARCH(1,1) or an ARMA(1,1)-GARCH(1,1) model. There is no situation where both ARCH-LM & LB and Li-Mak tests are applicable, so you never need to choose between better and worse tests, only between valid and invalid tests (which is an obvious choice).
*squared in case of the Ljung-Box test