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Title: Studying general multivariate dependence using associated copulas with applications to financial time series
Author: Salazar Flores, Yuri
ISNI:       0000 0004 2741 8044
Awarding Body: University of Essex
Current Institution: University of Essex
Date of Award: 2012
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In this thesis we study the general multivariate dependence of a random vector using associated copulas. The analysis of multivariate tail dependence has been centered in the positive case. To address this issue, we define the concept of gen- eral dependence and its corresponding probability functions. We prove a version of Sklar's Theorem that links these probability functions with its marginals using the associated copulas. We extend definitions and results from positive to the general dependence case. This includes associated tail dependence functions and associated tail dependence coefficients. We derive the relationships among associated copulas and obtain sev- eral results involving these copulas. We study the associated copulas of several copula models. This includes the perfect dependence cases, elliptical copulas, cop- ula models based on Laplace transforms, vine copulas and Marshall-Olkin copulas. For all these examples we analyse their tail dependence and obtain the correspond- ing tail dependence functions. We then extend several nonparametric estimators to the tail dependence func- tion in the general dependence case, and, using the results obtained in this work, we introudce new estimators. We use two optimisation methods for these esti- mators and run a simulation study to assess their performance for three levels of tail dependence and three sample sizes. With this simulation study we obtain an optimal estimator for each level of tail dependence. We use these estimators in two financial time series examples. In the first example we study the tail depen- dence structure between volatility indices and their corresponding stock market indices. In the second one between gold and other financial indices. With the results obtained in this thesis, it was possible to determine the existence of asym- metric negative tail dependence for both examples. Overlooking this feature can have undesirable consequences when modelling this data.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available