Characterizations of Multivariate Tail Dependence

Characterizations of Multivariate Tail Dependence: On theory and inference to assess extremal dependence structures

van der Zee, Carina (TU Delft Electrical Engineering, Mathematics and Computer Science)

Kurowicka, Dorota (mentor)
Cai, Juanjuan (mentor)

Delft University of Technology

2018-07-25

This thesis gathers, develops and evaluates several characterizations of multivariate tail dependence. It is established that the stable tail dependence function (STDF) is a suitable copula-based dependence function that fully captures the multivariate extremal dependence structure in all dimensions d≥2 and can be used to visualize the tail dependence structure for bivariate and trivariate problems. Based on the STDF, we propose a multivariate tail dependence coefficient (TDC) as an extension of the well-known bivariate TDC. Importantly, we show that the proposed measure can identify tail independence in all dimensions d≥2, similar to its bivariate variant. The performance of nonparametric estimators for the STDF and, inherently, the multivariate TDC, is assessed with an extensive simulation study, including smoothed and bias-corrected versions of the empirical STDF. Based on the estimators for the STDF and the multivariate TDC, test statistics under the null hypothesis of tail independence are developed and evaluated in another simulation study. The STDF-based estimation and testing procedures are applied to foreign exchange (FX) data to characterize the tail dependence structure between three European FX rates and five worldwide FX rates.

extreme value copula
stable tail dependence function
tail dependence coefficient
tail dependence testing

http://resolver.tudelft.nl/uuid:89b598fe-1631-4aae-97f4-8dede69d7490

Student theses

master thesis

© 2018 Carina van der Zee