Goodness-of-fit testing of copulas using quasi-Monte Carlo methods
Multivariate models with dependent variables are popular in financial industry, geostatistic, hydrology, insurance mathematics, medicine, and reliability theory. Simulations of copulas can be done by Monte Carlo methods or quasi-Monte Carlo methods. Goodness-of-it test can be used to find the best simulation algorithms for copulas. Since most of the goodness-of-fit tests are designed for univariate distributions, dimension reduction or bootstrapping is normally used in existing tests. We introduce a new goodness-of-fit test based on collision test and low-discrepancy sequences, and present numerical results to compare its efficiency with some current tests.