Gaussian copula of stable random vectors and application

Year 2020, Volume: 49 Issue: 2, 887 - 901, 02.04.2020

Phuc Ho Dang Truc Giang Vo Thi

https://doi.org/10.15672/hujms.621919

Abstract

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.

Keywords

stable distributions, multivariate density function, GPSdata, stock market, portfolio selection

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.

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