Thời gian: 14h Thứ 5, ngày 03/11/2022

Địa điểm: Phòng 507 nhà A6

Link online Googlemeet: https://meet.google.com/wfg-eqph-ncd

Abstract: Copula is used to model the dependence between marginals of a random vector, and construct multidimensional distributions with specified dependence and arbitrary marginal laws. Stable distributions are natural heavy tailed extensions of normal distributions and have attracted plenty of attention in practice. Studying two above concepts obtained important results for multivariate stable distribution.

Firstly, the existence of a Gaussian copula of an α-stable random vector: For every number α in (0,2], there exists an α-stable random vector W such that a Gaussian copula C of a normally distributed random vector with positive defined covariance matrix is also the copula of W. Moreover, a random vector with α- stable marginals and Gaussian copula has α-stable distribution.

Secondly, the existence of a transformation which turns a stable random vector into a sub-Gaussian random vector: Let X be a stable random vector in such that its marginals's skewness parameters different from pm 1,then there exists an invertible differentiable transformation K: R^d to R^d such that the random vector Y = K(X) is a sub-Gaussian random vector.This bijective transformation is built up step-by-step with closed-formula.

From two above results, a computation formula of density function is proposed, that can be applied to estimate probability density function of data with multivariate stable distribution in two cases: stable random vector has Gaussian copula and stable random vector has marginals's skewness parameters different from pm 1. Besides, we suggest procedures for conducting the goodness-of-fit testing on stable distribution of multivariate data.

Some data sets are applied with following outcomes: GPS data (with two components longitude and latitude) and exchange rates (include USD and RUB) have stable distribution; stock prices of 4 stocks(BID, VCB, FLC, VNM) or 6 stocks (AKRXQ, AMZN, AAPL, FB, MSFT, MSFT, WMMVE) have stable distribution. But, stock prices of5 stocks (JNJ, XOM, FB, HD, PPG) do not have stable distribution.