Goodness-of-fit tests for parametric families of Archimedean copulas

This paper suggests a goodness-of-fit test for parametric families of Archimedean copulas for high dimensional distributions. The test statistic is based on the classical chi-square-statistic but has a nonstandard asymptotic distribution. Monte-Carlo simulations show that the test keeps the nominal size and has high power to detect misspecified copulas. An empirical illustration on the return distribution of the USA S&P500 Chemical stocks is given. The results have interesting implications for portfolio management.