why in an ARIMA-GARCH structure I have to assume an error distribution to run the estimation while in a simple ARIMA model it is not required?
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Simple ARIMA model can be estimated using OLS methods. MA models (or ARMA model) can be estimated using iterative OLS, which provide similar results if MLE is used, assuming that error terms follows normal distribution with constant variance.
Since, GARCH model assumes that conditional variance is not constant. Such dynamic behaviour in volatility can not be accommodated into OLS method. Therefore, we use MLE for GARCH models, which mandatorily require assumption about distribution of error terms.
I would imagine this depends on the package you are using to estimate the ARIMA model and the GARCH model. Often, there is an implicit error distribution used in the fitting process. Many packages will not allow different error distributions, and will assume a Normal error distribution.
So, for example, if you look at the MATLAB ARIMA time series modelling, you can see that you can specify an error distribution (see halfway down https://uk.mathworks.com/help/econ/arima-class.html where you can choose 'Gaussian' or 'T').