Exploring the total positivity of yields correlations

We test the plausibility of the total positivity assumption of interest rates changes recently introduced in order to justify the presence of shift, slope and curvature for yield curves. To this aim, we introduce and discuss a test of total positivity of order (Formula presented.) for covariance and correlation matrices. The explicit expressions of the test statistics are given for Gaussian samples and an extension to a distribution-free framework is made via a bootstrap method. After exploring with simulation the robustness of such tests, we show using real data how it is realistic to assume that correlation matrices of interest rates changes are totally positive of order two. Conclusions on total positivity of order three are more controversial.