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I have read many questions about Gaussian and Gaussian copula. I really cannot figure out:

  1. when and when not to use Gaussian copula?
  2. If the margins are normal then we can use Gaussian to model the dependence structure. However, if they are not normal then we can transform them to normal and then use Gaussian model. However, in copula model, why do we need to transform the margins to uniform and then fit Gaussian copula? Also, if the margins are uniform then how we can use Gaussian where the margins must be normal?
Maryam
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  • Well, if you have a gaussian copula **and** gaussian marginals, then you have a multivariate normal distribution. But you could potentially have gaussian marginals but not a gaussian copula, and your procedure could be used to investigate that. An example is https://stats.stackexchange.com/questions/308775/conditional-expectation-of-two-identical-marginal-normal-random-variables/308831#308831 – kjetil b halvorsen Jun 29 '18 at 18:29
  • @kjetilbhalvorsen thank you so much for your comment. If the margins are uniforms, then how we can model them using the Gaussian copula, where Gaussian only accepted if the margins are normal? – Maryam Jun 29 '18 at 18:47
  • A copula does **by definition** have uniform marginals! As soon as you have transformed to uniform marginals, you can try different copula models and see which fits better. – kjetil b halvorsen Jun 29 '18 at 18:49
  • @kjetilbhalvorsen Thanks again. Ok. What I understand it, the copula is looking for dependence independently from margins. So, whatever the margins is, the copula does not matter. – Maryam Jun 29 '18 at 18:55
  • I do not understand " ... the copula does not matter"? The copula matters, because it describes the dependency! Copulas was invented to decouple the modelling of marginal distribution from the dependency modelling – kjetil b halvorsen Jun 29 '18 at 18:58
  • @kjetilbhalvorsen, Sorry. I meant that copula does not matter about the type of the margins. Hence, the copula is not affected by the margins. – Maryam Jun 29 '18 at 19:21

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