# Simultaneous estimation of ARMA and GARCH components

I am not allowed to comment on older questions relevant to this question, therefore I ask this myself. The question was dealt with here, here and here with a clear result: the ARMA part should be estimated simulataneously. However, I wonder how to show or prove clearcut that the ARMA coefficients are inconsistent and the ACF bounds are invalid? Further, why is it not possible to assume the regular null distribution under GARCH-type errors when conducting the Ljung-Box test? Does someone have relevant resources related to this issues?