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Model selection in sparse high-dimensional vine copula models with an application to portfolio risk

Author

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  • Nagler, T.
  • Bumann, C.
  • Czado, C.

Abstract

Vine copulas allow the construction of flexible dependence models for an arbitrary number of variables using only bivariate building blocks. The number of parameters in a vine copula model increases quadratically with the dimension, which poses challenges in high-dimensional applications. To alleviate the computational burden and risk of overfitting, we propose a modified Bayesian information criterion (BIC) tailored to sparse vine copula models. We argue that this criterion can consistently distinguish between the true and alternative models under less stringent conditions than the classical BIC. The criterion suggested here can further be used to select the hyper-parameters of sparse model classes, such as truncated and thresholded vine copulas. We present a computationally efficient implementation and illustrate the benefits of the proposed concepts with a case study where we model the dependence in a large portfolio.

Suggested Citation

  • Nagler, T. & Bumann, C. & Czado, C., 2019. "Model selection in sparse high-dimensional vine copula models with an application to portfolio risk," Journal of Multivariate Analysis, Elsevier, vol. 172(C), pages 180-192.
    • Handle: RePEc:eee:jmvana:v:172:y:2019:i:c:p:180-192
    DOI: 10.1016/j.jmva.2019.03.004
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    Citations

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    Cited by:

    1. Sahamkhadam, Maziar & Stephan, Andreas & Östermark, Ralf, 2022. "Copula-based Black–Litterman portfolio optimization," European Journal of Operational Research, Elsevier, vol. 297(3), pages 1055-1070.
    2. Jie Cheng, 2024. "Evaluating Density Forecasts Using Weighted Multivariate Scores in a Risk Management Context," Computational Economics, Springer;Society for Computational Economics, vol. 64(6), pages 3617-3643, December.
    3. Zhengyang Fan & Ran Ji & Miguel A. Lejeune, 2024. "Distributionally Robust Portfolio Optimization under Marginal and Copula Ambiguity," Journal of Optimization Theory and Applications, Springer, vol. 203(3), pages 2870-2907, December.
    4. Kiriliouk, Anna & Lee, Jeongjin & Segers, Johan, 2023. "X-Vine Models for Multivariate Extremes," LIDAM Discussion Papers ISBA 2023038, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Himchan Jeong & Dipak Dey, 2020. "Application of a Vine Copula for Multi-Line Insurance Reserving," Risks, MDPI, vol. 8(4), pages 1-23, October.
    6. Kreuzer, Alexander & Czado, Claudia, 2021. "Bayesian inference for a single factor copula stochastic volatility model using Hamiltonian Monte Carlo," Econometrics and Statistics, Elsevier, vol. 19(C), pages 130-150.
    7. Chang, Bo & Joe, Harry, 2019. "Prediction based on conditional distributions of vine copulas," Computational Statistics & Data Analysis, Elsevier, vol. 139(C), pages 45-63.
    8. Hans Lööf & Maziar Sahamkhadam & Andreas Stephan, 2023. "Incorporating ESG into Optimal Stock Portfolios for the Global Timber & Forestry Industry," Journal of Forest Economics, now publishers, vol. 38(2), pages 133-157, June.
    9. Sahin, Özge & Czado, Claudia, 2022. "Vine copula mixture models and clustering for non-Gaussian data," Econometrics and Statistics, Elsevier, vol. 22(C), pages 136-158.
    10. Bax, Karoline & Sahin, Özge & Czado, Claudia & Paterlini, Sandra, 2023. "ESG, risk, and (tail) dependence," International Review of Financial Analysis, Elsevier, vol. 87(C).
    11. Steffen Nico & Dickhaus Thorsten, 2020. "Optimizing effective numbers of tests by vine copula modeling," Dependence Modeling, De Gruyter, vol. 8(1), pages 172-185, January.
    12. Jain, Prachi & Maitra, Debasish, 2023. "Risk implications of dependence in the commodities: A copula-based analysis," Global Finance Journal, Elsevier, vol. 57(C).
    13. Savinov, Evgeniy & Shamraeva, Victoria, 2023. "On a Rosenblatt-type transformation of multivariate copulas," Econometrics and Statistics, Elsevier, vol. 25(C), pages 39-48.
    14. Steffen Nico & Dickhaus Thorsten, 2020. "Optimizing effective numbers of tests by vine copula modeling," Dependence Modeling, De Gruyter, vol. 8(1), pages 172-185, January.

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