I am modelling a set of time-series, and understand various models (ARIMA, AR, GARCH) allow for the inclusion of non-Gaussian error distributions. I am aware that, after fitting a time-series model, we should perform residual analysis, checking for no correlation, mean 0 and so on.
I was wondering if, given a time-series, there was anything that suggests what error distribution to use before fitting a model? As far as I am aware, simply looking at the distribution of the time-series values is not applicable, as we are modelling errors, not the series it's self.
Packages such as 'rugarch' offer a range of error distributions - Gaussian, t, skewed-t, normal inverse Gaussian and so on, but is there any way to know which of these might best suit a data-set, without trying each of them and checking what works best?