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?
