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I am using the R "rugarch" package to fit hybrid ARMA+GARCH models.
How should I test for the standardized residuals from the fitted hybrid ARMA+GARCH models to follow the following distributions?
I read the "rugarch" documentation but found nothing on the topic.
The fact that the data was generated as standardized residuals from an ARMA-GARCH model does not affect how you test distributional assumptions. You can still apply the classical approaches.
Therefore, your question is: How do I test whether a particular data sample comes from a particular distribution? This is a standard question covered in statistics textbooks. You could use Kolmogorov-Smirnov test, for example.
