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In the image below is a mixed vine copula composed of 3 copulae, therefore 3 marginals. It shows the 2d marginals and 100 samples of a 3d mixed vine.

enter image description here

Without being told its a vine copula, how would someone know that it is specifically a vine copula and not just 3 regular copula for 3 different random variables plotted separately?

Optional, guess the marginal distributions, and guess the 3 copula pairs

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    $\begingroup$ Are you literally putting on a contest of guessing models for simulated data, or are you actually just trying to figure out a model for a real dataset? In the latter case, the point isn't to guess that the data "comes from" a vine copula, but that a vine copula is a useful model for that data, even if it doesn't literally come from a vine copula. $\endgroup$
    – Chris Haug
    Commented Jul 29, 2020 at 15:17
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    $\begingroup$ That's my point, it doesn't matter that it "is" a vine; vines are general and flexible models, and they can work well for data that are not literally simulated from a vine. If you're asking, "how can I tell from these pictures that a vine will work well?", to be honest I don't know that anyone can. That's what goodness of fit tests, information criteria, out of sample testing with multivariate proper scoring rules, etc. are for. I suppose these pictures do show that a single copula of the usual families will not be sufficiently flexible because of the differences in types of relations. $\endgroup$
    – Chris Haug
    Commented Jul 29, 2020 at 15:56
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    $\begingroup$ So, a vine copula is a copula. There is a single copula that corresponds to every vine. It is just not typically one of the few "named" copulas. Vines are a convenient way to build complicated copulas out of basic bivariate ones. There is no "mistake" in saying that the data in the picture was generated "from a copula". $\endgroup$
    – Chris Haug
    Commented Jul 29, 2020 at 16:15
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    $\begingroup$ They are named after the types of graphs that arise in describing which pairs of variables are modeled by each copula: en.wikipedia.org/wiki/Vine_copula $\endgroup$
    – Chris Haug
    Commented Jul 29, 2020 at 18:55
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    $\begingroup$ For your question, the graph does not show the full vine as it does not include the conditional plot. However, we almost do not care whether this plot came from a vine copula or not. All that we are interested in is how vine copula can best model our data. $\endgroup$
    – Maryam
    Commented Aug 6, 2020 at 9:52

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A vine copula is a sequence of bivariate copulas, which is what is shown in the image. The proper depiction of the overall vine requires a graph tree linking the individual bivariate copulas

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  • $\begingroup$ @ Develarist : Great answers on Copula questions! I have some questions about this - can I ask them? $\endgroup$
    – stats_noob
    Commented Dec 18, 2021 at 7:43

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