Affiliations: [a] Statistics Discipline, Division of Science and Mathematics, University of Minnesota-Morris, Morris, MN, USA | [b] Cooperative Agricultural Research Center, College of Agriculture and Human Sciences, Prairie View A&M University, Prairie View, TX, USA
Corresponding author: Yoon-Sung Jung, Cooperative Agricultural Research Center, College of Agriculture and Human Sciences, Prairie View A&M University, Prairie View, TX 77446, USA. E-mail: [email protected].
Abstract: Directional dependence modeling has been applied to many research areas including economics, finance, biostatistics, and bioinformatics. The concept of directional dependence using copula regression functions has been introduced by Sungur . So we propose a new copula family which incorporates the truncation invariant structure  into the generalized Farlie-Gumbel-Morgenstern (FGM) distributions. The directional dependence of the new truncated invariant FGM copulas will be also introduced in this research. We will show that there exists a directional dependence in our truncation invariant FGM copulas using Foreign Currency Exchange Data of the Canadian Dollar (CAD/USD), the Japanese Yen (JPY/USD), and the Korean Won (KRW/USD).
Keywords: Copula, regression function, directional dependence, generalized FGM distribution