I hope everyone is doing well.
Citing Enders (2014) in the book Applied Econometric Time Series: "the Box–Jenkins approach also necessitates that the model be invertible" while discussing necessary conditions for AR, MA and ARMA models. Both in algebra and in code (R), this is relatively simple to verify for smaller models.
How should one proceed when dealing with models of the ARCH family (ARCH, GARCH, GARCH-M)? Given one has two equations (that one describing the behavior of the mean and that one describing the behavior of the variance), must invertibility be verified for both, or must one only verify it for the mean equation?