Test for Homogeneity of the Scale Matrix of Elliptical Tail Dependence with Application to Real Data

Test for Homogeneity of the Scale Matrix of Elliptical Tail Dependence with Application to Real Data

In finance, random quantities such as returns frequently exhibit asymmetry in their tail behavior. The tail behavior is described using an elliptical distribution owing to its heaviness. Moreover, elliptical distributions constitute a parametric model class of multivariate regular variations, and the scale matrix is important in determining the tail dependence. For testing the asymmetry of the tail dependence, we propose a likelihood ratio test that checks the homogeneity of the scale matrix in separate regions. Moreover, the proposed test is applied to a real dataset to investigate the asymmetry of tail dependence.

In finance, random quantities such as returns frequently exhibit asymmetry in their tail behavior. The tail behavior is described using an elliptical distribution owing to its heaviness. Moreover, elliptical distributions constitute a parametric model class of multivariate regular variations, and the scale matrix is important in determining the tail dependence. For testing the asymmetry of the tail dependence, we propose a likelihood ratio test that checks the homogeneity of the scale matrix in separate regions. Moreover, the proposed test is applied to a real dataset to investigate the asymmetry of tail dependence.