Journal of Data Science and Modeling

Some results on a generalized Archimedean copula with a stock market applicability

Document Type : Research Manuscript

Authors

Shaghayegh Molaei 1
Kianoush Fathi Vajargah 2
Hamid Mottaghi Golshan 3

1 Department of Statistics, North Tehran Branch, Islamic Azad University, Tehran, Iran

2 Department of Statistics, Islamic Azad University, North Tehran Branch, Tehran, Iran

3 Department of Mathematics, Shahriar Branch, Islamic Azad University, Shahriar, Iran

https://doi.org/10.22054/jdsm.2025.83879.1062
Abstract
This article examines the probability structure and dependency structure of a new family of Archimedean copula functions that are generated with two generators; this family is known as a generalization of the Archimedean copula functions and provides more tail dependence properties than the Archimedean family, making it more applicable. Using simulations, we compare a member of this family with various existing copula functions to highlight similarities and differences, and if the desired copula's scatter plot in terms of tail dependence is similar to the generalized Archimedean copula, we can fit the generalized Archimedean copula function to it.\\
Applications of this copula in the financial domain are demonstrated to improve the study of the dependence between indicators and to use this copula's advantageous characteristics. These theoretical concepts are validated by the numerical example provided at the end of the paper.
This article examines the probability structure and dependency structure of a new family of Archimedean copula functions that are generated with two generators; this family is known as a generalization of the Archimedean copula functions and provides more tail dependence properties than the Archimedean family, making it more applicable. Using simulations, we compare a member of this family with various existing copula functions to highlight similarities and differences, and if the desired copula's scatter plot in terms of tail dependence is similar to the generalized Archimedean copula, we can fit the generalized Archimedean copula function to it.\\

Keywords

Copula
Archimedean copula
Generalized Architecture copulas
Tail dependence
Subjects

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