Truncation invariant copulas for modeling directional dependence: Application to foreign currency exchange data
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).