I read from "Pair-copula constructions of multiple dependence", the following statement:

"The likelihood of the Clayton copula is lower than that of the Student copula (39.72 vs. 47.81). However, since the two copulae are non-nested we cannot really compare the likelihoods."

I really do not understand what does non-nested copulas and why in this case we cannot compare using the likelihoods method?

  • 1
    $\begingroup$ Here, "non-nested" seems to refer to "not belonging to the same family". The product copula for instance, is a special case of many other copulas such that changing the copula's parameter allows to continuously "move" from one to the other. $\endgroup$ – Ben Jan 16 at 21:48

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