Parameter Estimation and Application of the Multivariate Skew t-Copula

Abstract

Copula theory has got a rapid development in recent years. Most used copulas are symmetric: Archimedean are symmetric by construction while other continuous multivariate copulas are usually constructed from elliptical distributions and therefore are symmetric. From skewed copulas we can refer only to a copula introduced in [5], which the authors called skew t-copula. The construction of it differs from our approach. We introduce a multivariate t-copula which is based on the skew t-distribution introduced in [1]. Parameters of the copula have been estimated by method of moments and a simulation rule is given. The behaviour of estimates of the shape parameter of the skewed t-distribution is illustrated by simulation. The skew t-copula is used for modelling real data.

Gold and Government Bonds as Safe-Haven Assets Against Stock Market Turbulence in China

“…For instance, Demarta and McNeil (2005) suggested a skew-t copula in terms of a Gaussian mixture representation. Kollo and Pettere (2010) proposed a multivariate skew-t copula, whereas Smith et al (2012) established skew-t copulas. Christoffersen et al (2012) proposed a dynamic asymmetric copula model to describe not only long-term but also shortterm dynamic correlation.…”

“…Many skewed/fat-tailed distributions were suggested to interpret the dynamic nature of asset returns (Kollo & Pettere, 2010). Copula functions with skewed/fat-tailed distribution are widely suggested in finance, particularly in the field of risk management (Azzalini & Capitanio, 2003;Christoffersen & Langlois, 2013).…”

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“…These data allow accomplishing data simulation with copula approach (normal copula used). Further considerations about the approach used are explained in the paper by Kollo and Pettere (2009).…”

A Time-Varying Multivariate Noncentral Contaminated Normal Copula Model and Its Application to the Visualized Dependence Analysis of Hong Kong Stock Markets

“…e multivariate skew-t-copula is the copula of the multivariate skew-t distribution, such as Demarta and McNeil [3] proposed the copula of the multivariate generalized hyperbolic skew-t (GHST) distribution of Barndorff-Nielsen [4]. Kollo and Pettere [5] propose the copula of the multivariate skew-t distribution of Azzalini and Capitanio [6]; Smith et al [7] put forth the copula of the multivariate skew-t distribution of Sahu et al [8]; and Liu et al [9] advanced the copula of the multivariate extended skew-t (EST) distribution by Arellano-Valle and Genton [10].…”