Testing constant cross-sectional dependence with time-varying marginal distributions in parametric models

Abstract This paper proposes parametric two-step procedures for assessing the stability of cross-sectional dependency measures in the presence of potential breaks in the marginal distributions. The procedures are based on formerly proposed sup-LR tests in which restricted and unrestricted likelihood functions are compared with each other. First, we show theoretically that standard asymptotics do not hold in this situation. We propose a suitable bootstrap scheme and derive test statistics in different commonly used settings. The properties of the test statistics and precision of the associated change-point estimator are analysed and compared with existing non-parametric methods in various Monte Carlo simulations. These studies reveal advantages in test power for higher-dimensional data and an almost uniform superiority of the sup-LR test in terms of precision of the change-point estimator. We then apply this method to equity returns of European banks during the financial crisis of 2008.