Abstract
The selection of copulas is an important aspect of dependence modeling issues. In many practical applications, only a limited number of copulas is tested and the copula with the best result for a goodness-of-fit test is chosen, which, however, does not always lead to the best possible fit. In this paper we develop a practical and logical method for improving the goodness-of-fit of a particular Archimedean copula by means of transforms. In order to do this, we introduce concordance invariant transforms which can also be tail dependence preserving, based on an analysis on the λ-function, \({\lambda=\frac{\varphi}{\varphi'}}\), where \({\varphi}\) is the Archimedean generator. The methodology is applied to the data set studied in Cook and Johnson (J R Stat Soc B 43:210–218, 1981) and Genest and Rivest (J Am Stat Assoc 88:1043–1043, 1993), where we improve the fit of the Frank copula and obtain statistically significant results.
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Michiels, F., De Schepper, A. How to improve the fit of Archimedean copulas by means of transforms. Stat Papers 53, 345–355 (2012). https://doi.org/10.1007/s00362-010-0341-6
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DOI: https://doi.org/10.1007/s00362-010-0341-6