Year 2020, Volume 49 , Issue 2, Pages 887 - 901 2020-04-02

Gaussian copula of stable random vectors and application

Phuc HO DANG [1] , Truc Giang VO THİ [2]


In this paper, we present a new method to investigate data of multivariate heavy-tailed distributions. We show that for any given number $\alpha \in (0;2]$, each Gaussian copula is also the copula of an $\alpha$-stable random vector. Simultaneously, every random vector is $\alpha$-stable if its marginals are $\alpha$-stable and its copula is a Gaussian copula. The result is used to build up a formula representing density functions of $\alpha$-stable random vectors with Gaussian copula. Adopting a new tool, the paper points out that pairs of GPS signals recording latitude and longitude of a fixed point have two-dimensional stable distribution, and in the most of cases, vectors of daily returns in stock market data have multivariate stable distributions with Gaussian copulas.
stable distributions, multivariate density function, GPSdata, stock market, portfolio selection
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Primary Language en
Subjects Statistics and Probability
Journal Section Statistics
Authors

Orcid: 0000-0003-4415-9104
Author: Phuc HO DANG (Primary Author)
Institution: Ha Noi Institute of Mathematics, VAST
Country: Vietnam


Orcid: 0000-0002-2848-2748
Author: Truc Giang VO THİ
Institution: Tien Giang University
Country: Vietnam


Supporting Institution NAFOSTED, the Vietnam National Foundation for Sciences and Technology Development
Project Number 101.03-2017.07.
Thanks The study was partially supported by NAFOSTED, the Vietnam National Foundation for Sciences and Technology Development, under Grant number 101.03-2017.07. Thanks are due to Dr. Bui Quang Nam for the sharing the GPS data used in the application part of this study, and also to anonymous reviewers who gave valuable comments to make the article improved.
Dates

Publication Date : April 2, 2020

Bibtex @research article { hujms621919, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {887 - 901}, doi = {10.15672/hujms.621919}, title = {Gaussian copula of stable random vectors and application}, key = {cite}, author = {Ho Dang, Phuc and Vo Thi̇, Truc Giang} }
APA Ho Dang, P , Vo Thi̇, T . (2020). Gaussian copula of stable random vectors and application . Hacettepe Journal of Mathematics and Statistics , 49 (2) , 887-901 . DOI: 10.15672/hujms.621919
MLA Ho Dang, P , Vo Thi̇, T . "Gaussian copula of stable random vectors and application" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 887-901 <https://dergipark.org.tr/en/pub/hujms/issue/53568/621919>
Chicago Ho Dang, P , Vo Thi̇, T . "Gaussian copula of stable random vectors and application". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 887-901
RIS TY - JOUR T1 - Gaussian copula of stable random vectors and application AU - Phuc Ho Dang , Truc Giang Vo Thi̇ Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.621919 DO - 10.15672/hujms.621919 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 887 EP - 901 VL - 49 IS - 2 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.621919 UR - https://doi.org/10.15672/hujms.621919 Y2 - 2020 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Gaussian copula of stable random vectors and application %A Phuc Ho Dang , Truc Giang Vo Thi̇ %T Gaussian copula of stable random vectors and application %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 2 %R doi: 10.15672/hujms.621919 %U 10.15672/hujms.621919
ISNAD Ho Dang, Phuc , Vo Thi̇, Truc Giang . "Gaussian copula of stable random vectors and application". Hacettepe Journal of Mathematics and Statistics 49 / 2 (April 2020): 887-901 . https://doi.org/10.15672/hujms.621919
AMA Ho Dang P , Vo Thi̇ T . Gaussian copula of stable random vectors and application. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 887-901.
Vancouver Ho Dang P , Vo Thi̇ T . Gaussian copula of stable random vectors and application. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 887-901.