I am currently using (multivariate) mixture copulas to model a financial data set.
The mixture has two components as follows:
$$C_{mixture}=wC_1+(1-w)C_2$$
where $C_1$ and $C_2$ are copulas. I have closed form solutions for the tail dependence coefficients of both copulas. Are there any general solutions for the tail dependence of the mixture?
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$\begingroup$ What about example 3.2.3 here? $\endgroup$– eric_kernfeldApr 18, 2016 at 20:07
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$\begingroup$ Do you think this can be generalized to more than two dimensions? $\endgroup$– InfiniteVarianceApr 18, 2016 at 20:19
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1$\begingroup$ @eric Oh my. Grossmass is using $\lambda$ both as a mixing proportion and as the measure of tail dependence in the same formula (albeit with subscripts to distinguish upper and lower tail dependence). That's just awful. (How did Hardle allow it to get to the point of submission in that terrible state?) $\endgroup$– Glen_bApr 19, 2016 at 0:52
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$\begingroup$ So given that tail dependence is always a pairwise concept to me it comes down to the follwing question: Is the formula stated (tail dependence of mixture equals weighted tail dependence, where the weights are the mixture weights) applicable in higher dimension. The closed form solution I mentioned is already for pairs of variables in a multivariate copula context. $\endgroup$– InfiniteVarianceApr 19, 2016 at 11:07
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$\begingroup$ @InfiniteVariance If you are dealing with $Y = [y_1... y_D]$, you could just define $X = [y_j, y_k]$ and apply the results to $X$. Does that give you what you need? $\endgroup$– eric_kernfeldApr 19, 2016 at 19:17
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