Vine copula models with GLM and sparsity

ABSTRACT

Vine copula provides a flexible tool to capture asymmetry in modeling multivariate distributions. Nevertheless, its flexibility is achieved at the expense of exponentially increasing complexity of the model. To alleviate this issue, the simplifying assumption (SA) is commonly adapted in specific applications of vine copula models. In this paper, generalized linear models (GLMs) are proposed for the parameters in conditional bivariate copulas to relax the SA. In the spirit of the principle of parsimony, a regularization methodology is developed to control the number of parameters, leading to sparse vine copula models. The conventional vine copula with the SA, the proposed GLM-based vine copula, and the sparse vine copula are applied to several financial datasets, and the results show that our proposed models outperform the one with SA significantly in terms of the Bayesian information criterion.

KEYWORDS:

• Generalized linear model
• penalized MLE
• vine copula.

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E05
• 62E17
• 62H20

Acknowledgments

The authors are sincerely grateful for the comments from the anonymous referee and the Editor. All the three authors thank the financial support from the Society of Actuaries Centers of Actuarial Excellence Research Grant. In addition, D. Han acknowledges financial support from the Department of Statistics and Actuarial Science, University of Waterloo. Both K.S. Tan and C. Weng thank the financial support from the Natural Sciences and Engineering Research Council of Canada (PIN-220010 and NSERC-RGPIN-399399-2011, respectively).