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A goodness of fit test for copulas based on Rosenblatt’s transformation. (English) Zbl 1162.62343
Summary: A goodness of fit test for copulas based on Rosenblatt’s transformation is investigated. This test performs well if the marginal distribution functions are known and are used in the test statistic. If the marginal distribution functions are unknown and are replaced by their empirical estimates, then the test’s properties change significantly. This is shown in detail by simulation for special cases. A bootstrap version of the test is suggested and it is shown by simulation that it performs well. An empirical application of this test to daily returns of German assets reveals that a Gaussian copula is unsuitable to describe their dependence structure. A $$t_\nu$$-copula with low degrees of freedom such as $$\nu =4$$ or 5 fits the data in some cases.

##### MSC:
 62G10 Nonparametric hypothesis testing 62F40 Bootstrap, jackknife and other resampling methods 62F03 Parametric hypothesis testing 65C60 Computational problems in statistics (MSC2010) 62P05 Applications of statistics to actuarial sciences and financial mathematics
bootstrap
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