  Visualization and assessment of copula structures are crucial for accurately
understanding and modeling the dependencies in multivariate data analysis. In
this paper, we introduce an innovative method that employs functional boxplots
and rank-based testing procedures to evaluate copula symmetry. This approach is
specifically designed to assess key characteristics such as reflection
symmetry, radial symmetry, and joint symmetry. We first construct test
functions for each specific property and then investigate the asymptotic
properties of their empirical estimators. We demonstrate that the functional
boxplot of these sample test functions serves as an informative visualization
tool of a given copula structure, effectively measuring the departure from zero
of the test function. Furthermore, we introduce a nonparametric testing
procedure to assess the significance of deviations from symmetry, ensuring the
accuracy and reliability of our visualization method. Through extensive
simulation studies involving various copula models, we demonstrate the
effectiveness of our testing approach. Finally, we apply our visualization and
testing techniques to two real-world datasets: a nutritional habits survey with
five variables and wind speed data from three locations in Saudi Arabia.
