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If I want to forecast daily stock return let say Apple what would be the best GARCH model and why? (ARCH, GARCH-M, IGARCH, EGARCH, TARCH etc)

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  • $\begingroup$ ARCH-variants aren't used to forecast returns, they're used to model volatilities...the last word in the acronym (heteroskedasticity) indicates this. $\endgroup$ – Chris Apr 9 at 18:03
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GARCH models are usually used to predict volatility, not returns.

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  • $\begingroup$ This is completely correct, but also not really an answer to the question. $\endgroup$ – Chris Taylor Apr 7 at 13:43
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    $\begingroup$ The question asks about using GARCH models for something they are not designed to do. It is impossible to answer. $\endgroup$ – Alex C Apr 8 at 14:24
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You cannot use GARCH. The models you mentioned are used for modelling the conditional volatility, which is time-varying and displays clustering,as Mandelbrot mentioned.

A common model is an ARIMA(p,q,1), where p the order of the AR component and q the MA component. Simply, it is an ARMA(p,q) on the first differences of the log prices. This is due to the non stationarity of the log prices that drive ACF and PACF being significant for a long period of time (known as long memory process). Hence the first differences make the process stationary "cutting" the PACF and ACF shortly. As a heuristic, you can use an ARIMA(1,1,1) model, but technically speaking someone has to check higher order models as well. Model selection criteria, such as AIC or BIC have to be used.

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