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Is there any scientific reason why a lot of studies and packages choose the ACF plot of the standardised residuals rather than the residuals themselves?

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Assumptions for parameter estimators in an ARMA-GARCH model are made on standardized innovations, not raw ones. ACF plot of standardized innovations allows assessing whether the model assumptions are violated or not, and hence whether parameter estimates (realizations of estimators) can be trusted. Therefore, it makes sense to inspect the ACF of standardized innovations.

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