A Suggested Statistical Test for Measuring Bivariate Nonlinear Dependence

Raul Matsushita, University of Brasilia
Annibal Figueiredo, University of Brasilia
Sergio Da Silva, Federal University of Santa Catarina

Abstract

We devise a new asymptotic statisticaltest to assess independence in bivariate continuous distributions. Our approach is based on the Cramér–von Mises test, in which the empirical process is viewed as the Kullback–Leibler divergence, that is, as the distance between the data under the independence hypothesis and the data empirically observed. 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 non-Gaussian. Our case is illustrated with high-frequency data from stocks listed on the NYSE that recently experienced so-called mini-flash crashes.