Conditional expectation formula of copulas for higher dimensions and its application

Atina Ahdika, Dedi Rosadi, Adhitya Ronnie Effendie, Gunardi -

Abstract


Due to its simple form, linear regression is the most commonly used model when dealing with a predictive model. However, there are some limitations to the model, such as the constraint of only being able to model variables that have a linear relationship, the assumption of normality on its error, and the multi-collinearity between independent variables which should not occur. One of the alternative models that is free from these limitations is the copula-based regression model defined by the conditional expectation formula of copulas. Leong and Valdez [Claims prediction using copula models, Insurance Math. Econom., 2005] [15] developed a conditional expectation formula of copulas for higher dimensions in the implicit form with bivariate case examples. Crane and Hoek [Conditional expectation formulae for copulas, Aust. N.Z.J. Stat, 2008] [5] provided conditional expectation formula of copulas explicitly for two dimensions with its examples. However, in practice, a predictive model often involves more than two variables, i.e. one dependent variable with more than one independent variable, including a copula-based regression model. With regard to these problems and the limitations of dimension in previous studies, our contribution in this study is extending the copula-based regression model for higher dimensions for class of Farlie-Gumbel-Morgenstern, elliptical, and Archimedean copula. We obtain a closed-form of conditional expectation formula of Farlie-Gumbel-Morgenstern, Gaussian, Student-t, and Clayton copula for n dimensions and provide the formula for Gumbel copula up to four dimensions. We apply our extended formula to estimate KRW/USD currency based on its association with CNY/USD and JPY/USD, and found that the extended function can be used quite accurately.


Full Text: PDF

Published: 2021-06-15

How to Cite this Article:

Atina Ahdika, Dedi Rosadi, Adhitya Ronnie Effendie, Gunardi -, Conditional expectation formula of copulas for higher dimensions and its application, J. Math. Comput. Sci., 11 (2021), 4877-4904

Copyright © 2021 Atina Ahdika, Dedi Rosadi, Adhitya Ronnie Effendie, Gunardi -. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

 

Copyright ©2022 JMCS