论文信息 - Hierarchical Archimedean Copulas for MATLAB and Octave: The HACopula Toolbox

Hierarchical Archimedean Copulas for MATLAB and Octave: The HACopula Toolbox

To extend the current implementation of copulas in MATLAB to non-elliptical distributions in arbitrary dimensions enabling for asymmetries in the tails, the toolbox HACopula provides functionality for modeling with hierarchical (or nested) Archimedean copulas. This includes their representation as MATLAB objects, evaluation, sampling, estimation and goodness-of-fit testing, as well as tools for their visual representation or computation of corresponding matrices of Kendall's tau and tail dependence coefficients. These are first presented in a quick-and-simple manner and then elaborated in more detail to show the full capability of HACopula. As an example, sampling, estimation and goodness-of-fit of a 100-dimensional hierarchical Archimedean copula is presented, including a speed up of its computationally most demanding part. The toolbox is also compatible with Octave, where no support for copulas in more than two dimensions is currently provided.

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

[2] Marius Hofert,et al. A stochastic representation and sampling algorithm for nested Archimedean copulas , 2012 .

[3] H. Joe. Multivariate models and dependence concepts , 1998 .

[4] Alexander J. McNeil,et al. Multivariate Archimedean copulas, $d$-monotone functions and $\ell_1$-norm symmetric distributions , 2009, 0908.3750.

[5] Jun Yan,et al. Enjoy the Joy of Copulas: With a Package copula , 2007 .

[6] C. Genest,et al. Rank-based methods for modeling dependence between loss triangles , 2016, European Actuarial Journal.

[7] Martin Holena,et al. An approach to structure determination and estimation of hierarchical Archimedean Copulas and its application to Bayesian classification , 2016, Journal of Intelligent Information Systems.

[8] Ostap Okhrin,et al. Hierarchical Archimedean Copulae: The HAC Package , 2012 .

[9] Jun Yan,et al. Modeling Multivariate Distributions with Continuous Margins Using the copula R Package , 2010 .

[10] A. McNeil. Sampling nested Archimedean copulas , 2008 .

[11] I. Olkin,et al. Families of Multivariate Distributions , 1988 .

[12] C. Kimberling. A probabilistic interpretation of complete monotonicity , 1974 .

[13] Jeffrey Sheen,et al. Conditional Systemic Risk with Penalized Copula , 2015 .