A test for Archimedeanity in bivariate copula models
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Date
2011-09-20
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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 satis es weak smoothness assumptions. A simulation study
is presented which illustrates the finite sample properties of the new test.
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Keywords
Archimedean Copula, associativity, functional delta method, multiplier bootstrap