||The assumption of multivariate ellipticity of financial returns has been the foundation of risk models for many decades. However, if this assumption is not met by the data, as is often the case, the implied correlation analysis may yield misleading results. For this reason we aim to study the dependence of the joint distribution of financial time series focusing on the quantiles dependence. The method we aim to employ in the study is dynamic copula quantile regression, a special case of nonlinear quantile regression. This method is able to characterize the whole distribution and allows different relationship between the regressor and the dependent variable at different quantiles. These properties are very appealing, especially in risk management and portfolio modelling. To avoid large unexpected losses, we are interested to know the type of dependence in the financial data, focusing on the lower tail dependence of the joint distribution. We believe that application of the copula quantile regression method will provide us more useful information than usual mean regressions.