Copula Modeling Dependence with Continuous Margins with Application by Using the Package R

Luseen Immanuel Kework

Abstract


 This paper presents a class of multivariate probability models, known as “copula models”. The aim of this paper is modeling dependence structure between random variables using copula. The copula-based modeling of multivariate distributions with continuous margins is presented as a succession of rank-based tests: a multivariate test of randomness followed by a test of mutual independence and a series of goodness-of-fit tests. All the tests under study are based on the empirical copula, which is a nonparametric rank-based estimator of the true unknown copula. The principles of the tests are recalled and their implementation in the copula package R is briefly described. Their use in the construction of a copula model from data is thoroughly illustrated on real financial and physical structure data. The majority of the results thereby suggest that the Clayton copula and the t – copula provides an adequate representation of the empirical dependence structures for the performance analytics data and the urine analysis data, respectively.

 

Keywords: copula, multivariate independence, pseudo-observations, rank-based tests, serial independence, goodness of fit.


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