A test for Archimedeanity in bivariate copula models

Abstract

We propose a new test for the hypothesis that a bivariate copula is an Archimedean copula. The test statistic is based on a combination of two measures resulting from the characterization of Archimedean copulas by the property of associativity and by a strict upper bound on the diagonal by the Fréchet-upper bound. We prove weak convergence of this statistic and show that the critical values of the corresponding test can be determined by the multiplier bootstrap method. The test is shown to be consistent against all departures from Archimedeanity if the copula satisfies weak smoothness assumptions. A simulation study is presented which illustrates the finite sample properties of the new test.

Goodness-of-Fit Tests for Multivariate Copula-Based Time Series Models

“…It has been proposed in Scaillet (2005) and Rémillard and Scaillet (2009) for i.i.d. data sets, and has been applied to different testing issues in Genest et al (2011);Bücher et al (2011Bücher et al ( , 2012, among others. The procedure has been generalized to the alpha-mixing case in Bücher and Ruppert (2013) with several further improvements in Bücher and Kojadinovic (2013).…”

On the estimation of Pareto fronts from the point of view of copula theory

“…(6). Some parametric methods have been proposed in order to fit univariate distributions and to obtain straightforward simple expressions for their inverse functions, see e.g.…”

“…If one would rather use the empirical copula, as discussed in the next Section, it is sufficient to compute the empirical copula and to estimate level lines from Eqs. (6) and (8).…”

“…Recent works exist in the bivariate case, see e.g. [6]. Otherwise a simple test is to compare visually the level curves of the empirical copula with those of the fitted Archimedean copula in the same spirit as the normal probability plot in dimension one.…”

A copula-based method for reliability sensitivity analysis of structural system with correlated failure modes

“…To overcome this problem, the Archimedean copulas are used as an alternative to solve the high-dimensional dependence modeling problem. The family of Archimedean copulas has been studied extensively by a number of authors including [2,4,7,22]. Well known representatives of the Archimedean family are GumbelHougaard, Frank and Clayton copula.…”