# Is there a copula that can estimate negative tail dependence?

I have encountered numerous copula estimators that can estimate time-invariant and time-varying linear and non-linear correlations on the interval $[-1,1]$, and these estimators are fully consistent with arbitrary univariate marginals and different forms of the bivariate joint distribution.

I have also encountered copulas (Gumbel, Clayton, and others) that can estimate time-varying lower and upper tail dependence on the interval $[0,1]$.

However, I believe that these tail dependence measures can only detect positive dependence.

Does there exist a time-invariant OR time-varying copula estimator that can detect negative dependence in the tails?

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Tail dependence coefficient is by definition non-negative. You need to formulate what do you mean by "negative dependence in the tails" as it's not obvious. – Alexey Kalmykov Jan 22 at 13:31