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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?

  • Skewed Normal ("snorm")
  • Skewed Student T ("sstd")
  • Generalized Error Distribution ("ged")
  • Skewed Generalized Error Distribution ("sged")

I read the "rugarch" documentation but found nothing on the topic.

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  • $\begingroup$ An alternative to specific tests would be the Pearson Adjusted Chi-Square Test for Goodness of Fit which is displayed automatically by the ugarchfit function. Anyway I would like to run more specific tests. $\endgroup$
    – msmna93
    Sep 27, 2016 at 21:25

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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.

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  • $\begingroup$ Ok, but can I use KS test also for skewed Student-T distribution? Moreover, could you indicate what tests are available for GED and sGED? I did not find any in statistics textbooks $\endgroup$
    – msmna93
    Sep 28, 2016 at 10:39
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    $\begingroup$ KS test can be used for any distribution. It does not have some standard distribution to which it would always apply. Therefore, it is a pretty flexible test. You just take your data and the reference distribution (e.g. GED or SGED) and carry out the test procedure. $\endgroup$ Sep 28, 2016 at 10:49

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