Application of Stable Random Vector with Gaussian Copula

Abstract

More and more real-world datasets have heavy-tailed distribution, while the calculations for these distributions in multi-dimensional cases are complex. This work shows a method to investigate data of multivariate heavy-tailed distributions. The sufficient condition for every a-stable random vector is that it has α-stable marginals and Gaussian copula. From that results, we have a procedure testing stable distribution of multi-dimensional data and a formula representing density functions of multivariate stable distribution. Adopted a new tool, datasets about daily returns of 4 stocks on HoSE and 3 grains were analyzed.