A goodness-of-fit test for copulas based on martingale transformation

This paper proposes an asymptotically distribution-free test for copulas with dynamic marginal distributions, such as GARCH and ARMA processes. The test is based on the empirical copula process with parametrically estimated marginal distributions. By applying the Khmaladze (1982, 1988, 1993) martingale transformation method, the transformed empirical process converges to a standard Gaussian process, so the resulting test statistics are asymptotically distribution-free. Monte Carlo simulations show that the test performs well in finite samples. An empirical application to test copulas between EUR/USD and GBP/USD exchange rates is provided. (C) 2019 Elsevier B.V. All rights reserved.