Modeling Directional Dependence: A Copula Approach

• Activity Number: 465
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Graphics
• Author(s): Engin Sungur*+ and Jessica Orth
• Companies: University of Minnesota and University of Iowa
• Keywords: Copulas ; Dependence Plots ; Directional dependence ; Jacobi rotations ; Angular correlation plots

Abstract

Understanding and modeling multivariate dependence structures depending upon the direction are challenging but an interest of theoretical and applied researchers. Directional dependence modeling is an effective approach on answering many research questions in various areas such as economics, finance, biostatistics, and bioinformatics. We formally define the directional dependence and introduce a parameterization through rotation angles to model it. A new class of copulas with directional dependence property has been constructed by using oblique Jacobi rotation of a Gaussian and uniform random vectors. The properties of this family are presented and possible applications are given. Also, a systematic approach to generate p-dimensional copulas under various directional dependence settings is introduced. This construction allows us to model and measure directional dependence in a meaningful way and leads to informative graphical displays.