Pós-Graduação em Estatística We devise a new asymptotic test to assess independence in bivariate continuous distributions. Our approach is based on the classical likelihood-ratio chi-square statistic, which is related to the Kullback-Leibler distance between two empirical distributions. Our test is distribution free and will prove to be more powerful than the classical Hoeffding-Blum-Kiefer-Rosenblatt test in detecting nonlinear contemporaneous dependence. We derive the theoretical characteristic function of the limit distribution of the test statistic and find the critical values through computer simulation. A Monte Carlo experiment is considered as assessing the validation and power performance of the test by assuming a bivariate nonlinear dependence structure with fat tails. Two extra examples, respectively, consider stationary and conditionally nonstationary series. Results confirm that our suggested test is consistent and powerful in the presence of bivariate nonlinear dependence even if the environment is nonGaussian. Our case is illustrated with high-frequency data from stocks listed on the NYSE that recently experienced so-called mini-flash crashes.
Referência: R. Matsushita, A. Figueiredo, S. Da Silva, A suggested statistical test for measuring bivariate nonlinear dependence, Physica A 391 (2012) 4891-4898.