| Penulis/Author |
ATINA AHDIKA (1); Prof. Dr.rer.nat. Dedi Rosadi, S.Si.,, M.Sc. (2) ; Dr. Adhitya Ronnie Effendie, S.Si., M.Si., M.Sc. (3); Prof. Dr. Drs. Gunardi, M.Si. (4) |
| Abstrak/Abstract |
Due to its simple form, linear regression is the most commonly used model when dealing with apredictive model. However, there are some limitations to the model, such as the constraint of only being able tomodel variables that have a linear relationship, the assumption of normality on its error, and the multi-collinearitybetween independent variables which should not occur. One of the alternative models that is free from theselimitations is the copula-based regression model defined by the conditional expectation formula of copulas. Leongand Valdez [Claims prediction using copula models, Insurance Math. Econom., 2005] [15] developed a conditionalexpectation formula of copulas for higher dimensions in the implicit form with bivariate case examples. Crane andHoek [Conditional expectation formulae for copulas, Aust. N.Z.J. Stat, 2008] [5] provided conditional expectationformula of copulas explicitly for two dimensions with its examples. However, in practice, a predictive model ofteninvolves more than two variables, i.e. one dependent variable with more than one independent variable, includinga copula-based regression model. With regard to these problems and the limitations of dimension in previousstudies, our contribution in this study is extending the copula-based regression model for higher dimensions forclass of Farlie-Gumbel-Morgenstern, elliptical, and Archimedean copula. We obtain a closed-form of conditionalexpectation formula of Farlie-Gumbel-Morgenstern, Gaussian, Student-t, and Clayton copula forndimensionsand provide the formula for Gumbel copula up to four dimensions. We apply our extended formula to estimateKRW/USD currency based on its association with CNY/USD and JPY/USD, and found that the extended function can be used quite accurately |
