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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.

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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

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  • $\begingroup$ Thank you for your answer. This means ARCH-LM and LB tests are to be applied on e.g. raw returns (or on residuals). If ARCH effects are identified I can fit e.g. a GARCH model and afterwards I can test for any remaining conditional heteroscedasticity using the Li-Mak test. Is that right? $\endgroup$ Nov 28, 2021 at 15:56
  • $\begingroup$ @Programm_Newbie9196, exactly. This is what you would also find in other threads that mention Li-Mak test. (Many of these contain my answers.) $\endgroup$ Nov 28, 2021 at 16:03
  • $\begingroup$ Amazing. I've already seen many of your answers and they helped me a lot. Thanks again and enjoy your sunday! $\endgroup$ Nov 28, 2021 at 16:08

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