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Nonparametric confidence intervals for tail dependence based on copulas. (English. French summary) Zbl 1358.62049

Summary: We propose nonparametric asymptotic confidence intervals for the upper and lower tail dependence coefficients. These latter are obtained from confidence bands established for the copula function itself and based upon three kernel-type estimators. We show the performance of these confidence intervals through a simulation study. We also apply these results to financial data stemming from the CAC 40 stock index which reveals the existence of extreme dependence between larger values of the opening and closing prices for this index during the considered period.

MSC:

62G15 Nonparametric tolerance and confidence regions
62H20 Measures of association (correlation, canonical correlation, etc.)
62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
62P05 Applications of statistics to actuarial sciences and financial mathematics
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Full Text: Euclid