Pssst... Don't tell anyone I told you this... But 69% of "quant trading" is Excel hooked up to TT.
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there is some cute (but simple) math in how you make an n-period ahead vol forecast, and some cute (annoying) math in how you jointly estimate the parameters but the model itself is dumb af
also you should never jointly estimate the parameters, just plug in some sensible numbers and go
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tired: apparel models are dumb af wired: statistical models are dumb af
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I think the key determinant here is the parameter persistence/forecastability. If you think params are persistent and forecastable then it’s prob worth trying to estimate them. But with garch MLE params aren’t very persistent
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