Multivariate Skew Normal Copula for Asymmetric Dependence: Estimation and Application

The exchangeability and radial symmetry assumptions on the dependence structure of the multivariate data are restrictive in practical situations where the variables of interest are not likely to be associated to each other in an identical manner. In this paper, we propose a flexible class of multivariate skew normal copulas to model high-dimensional asymmetric dependence patterns. The proposed copulas have two sets of parameters capturing asymmetric dependence, one for association between the variables and the other for skewness of the variables. In order to efficiently estimate the two sets of parameters, we introduce the block coordinate ascent algorithm and discuss its convergence property. The proposed class of multivariate skew normal copulas is illustrated using a real data set.

[1]  Engin A. Sungur.  A Note on Directional Dependence in Regression Setting , 2005 .

[2]  Campbell R. Harvey,et al.  Forecasting International Equity Correlations , 1994 .

[3]  E. Luciano,et al.  Copula Methods in Finance: Cherubini/Copula , 2004 .

[4]  F. Longin,et al.  Extreme Correlation of International Equity Markets , 2000 .

[5]  Yi Peng,et al.  Evaluation of clustering algorithms for financial risk analysis using MCDM methods , 2014, Inf. Sci..

[6]  T. Bedford,et al.  Vines: A new graphical model for dependent random variables , 2002 .

[7]  D. Oakes.  Multivariate survival distributions , 1994 .

[8]  Dag Tjøstheim,et al.  Model selection of copulas: AIC versus a cross validation copula information criterion , 2014 .

[9]  A. G. Vitushkin.  On Hilbert's thirteenth problem and related questions , 2004 .

[10]  Gunky Kim,et al.  Comparison of semiparametric and parametric methods for estimating copulas , 2007, Comput. Stat. Data Anal..

[11]  Pavel Krupskii,et al.  Structured factor copula models: Theory, inference and computation , 2015, J. Multivar. Anal..

[12]  Toshinao Yoshiba.  Maximum likelihood estimation of skew-t copulas with its applications to stock returns , 2018 .

[13]  Yang Chen,et al.  Pairwise comparison matrix in multiple criteria decision making , 2016 .

[14]  Vijay P. Singh,et al.  Bivariate rainfall frequency distributions using Archimedean copulas , 2007 .

[15]  Emiliano A. Valdez,et al.  Understanding Relationships Using Copulas , 1998 .

[16]  Biljana Mileva Boshkoska.  From Qualitative to Quantitative Evaluation Methods in Multi-criteria Decision Models , 2014 .

[17]  Christian Genest,et al.  Beyond simplified pair-copula constructions , 2012, J. Multivar. Anal..

[18]  Pavel Krupskii,et al.  Factor copula models for multivariate data , 2013, J. Multivar. Anal..

[19]  Engin A. Sungur.  Some Observations on Copula Regression Functions , 2005 .

[20]  Ulf Schepsmeier,et al.  Efficient information based goodness-of-fit tests for vine copula models with fixed margins: A comprehensive review , 2015, J. Multivar. Anal..

[22]  Yi Peng,et al.  Evaluation of Classification Algorithms Using MCDM and Rank Correlation , 2012, Int. J. Inf. Technol. Decis. Mak..

[23]  C. Genest,et al.  A semiparametric estimation procedure of dependence parameters in multivariate families of distributions , 1995 .

[24]  H. Joe.  Dependence Modeling with Copulas , 2014 .

[25]  Andrew J. Patton.  Modelling Asymmetric Exchange Rate Dependence , 2006 .

[26]  Tonghui Wang,et al.  Multiple Copula Regression Function and Directional Dependence Under Multivariate Non-exchangeable Copulas , 2016, Causal Inference in Econometrics.

[27]  B. Wu,et al.  Copula‐based regression models for a bivariate mixed discrete and continuous outcome , 2011, Statistics in medicine.

[28]  Luigi Grippof,et al.  Globally convergent block-coordinate techniques for unconstrained optimization , 1999 .

[29]  A. Azzalini.  A class of distributions which includes the normal ones , 1985 .

[30]  George G. Lorentz,et al.  Approximation of Functions , 1968 .

[31]  H. Akaike.  A new look at the statistical model identification , 1974 .

[32]  Eckhard Liebscher,et al.  Construction of asymmetric multivariate copulas , 2008 .

[33]  Alexander J. McNeil,et al.  From Archimedean to Liouville copulas , 2010, J. Multivar. Anal..

[34]  Vladik Kreinovich,et al.  Vine Copulas As a Way to Describe and Analyze Multi-Variate Dependence in Econometrics: Computational Motivation and Comparison with Bayesian Networks and Fuzzy Approaches , 2014, TES.

[35]  Tonghui Wang,et al.  Distribution of quadratic forms under skew normal settings , 2009, J. Multivar. Anal..

[36]  Jong-Min Kim,et al.  Analysis of directional dependence using asymmetric copula-based regression models , 2014 .

[37]  Claudia Czado,et al.  Simplified pair copula constructions - Limitations and extensions , 2013, J. Multivar. Anal..

[38]  A. Azzalini,et al.  The multivariate skew-normal distribution , 1996 .

[39]  Stéphane Girard,et al.  A flexible and tractable class of one-factor copulas , 2016, Stat. Comput..

[40]  A. Azzalini,et al.  Statistical applications of the multivariate skew normal distribution , 2009, 0911.2093.

[41]  Insuk Sohn,et al.  BMC Bioinformatics BioMed Central Methodology article A copula method for modeling directional dependence of genes , 2022 .

[42]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[43]  H. Joe.  Families of $m$-variate distributions with given margins and $m(m-1)/2$ bivariate dependence parameters , 1996 .