IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v172y2022ics016794732200041x.html
   My bibliography  Save this article

Regular vines with strongly chordal pattern of (conditional) independence

Author

Listed:
  • Zhu, Kailun
  • Kurowicka, Dorota

Abstract

Multivariate statistical models can be simplified by assuming that a pattern of conditional independence is presented in the given data. A popular way of capturing the (conditional) independence is to use probabilistic graphical models. The relationship between strongly chordal graphs and m-saturated vines is proved. Moreover, an algorithm to construct an m-saturated vine structure corresponding to strongly chordal graph is provided. This allows the reduction of regular vine copula models complexity. When the underlying data is sparse our approach leads to model estimation improvement when compared with current heuristic methods. Furthermore, due to reduction of model complexity it is possible to evaluate all vine structures as well as to fit non-simplified vines. These advantages have been shown in the simulated and real data examples.1

Suggested Citation

  • Zhu, Kailun & Kurowicka, Dorota, 2022. "Regular vines with strongly chordal pattern of (conditional) independence," Computational Statistics & Data Analysis, Elsevier, vol. 172(C).
  • Handle: RePEc:eee:csdana:v:172:y:2022:i:c:s016794732200041x
    DOI: 10.1016/j.csda.2022.107461
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016794732200041X
    Download Restriction: Full text for ScienceDirect subscribers only.

    File URL: https://libkey.io/10.1016/j.csda.2022.107461?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Cooke, R.M. & Kurowicka, D. & Wilson, K., 2015. "Sampling, conditionalizing, counting, merging, searching regular vines," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 4-18.
    2. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    3. Dißmann, J. & Brechmann, E.C. & Czado, C. & Kurowicka, D., 2013. "Selecting and estimating regular vine copulae and application to financial returns," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 52-69.
    4. Müller, Dominik & Czado, Claudia, 2019. "Dependence modelling in ultra high dimensions with vine copulas and the Graphical Lasso," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 211-232.
    5. Wille Anja & Bühlmann Peter, 2006. "Low-Order Conditional Independence Graphs for Inferring Genetic Networks," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 5(1), pages 1-34, January.
    6. Elif F. Acar & Radu V. Craiu & Fang Yao, 2011. "Dependence Calibration in Conditional Copulas: A Nonparametric Approach," Biometrics, The International Biometric Society, vol. 67(2), pages 445-453, June.
    7. Hobæk Haff, Ingrid & Aas, Kjersti & Frigessi, Arnoldo & Lacal, Virginia, 2016. "Structure learning in Bayesian Networks using regular vines," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 186-208.
    8. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    9. Acar, Elif F. & Genest, Christian & Nešlehová, Johanna, 2012. "Beyond simplified pair-copula constructions," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 74-90.
    10. Acar, Elif F. & Czado, Claudia & Lysy, Martin, 2019. "Flexible dynamic vine copula models for multivariate time series data," Econometrics and Statistics, Elsevier, vol. 12(C), pages 181-197.
    11. Stöber, Jakob & Joe, Harry & Czado, Claudia, 2013. "Simplified pair copula constructions—Limitations and extensions," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 101-118.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kajal Lahiri & Liu Yang, 2023. "Predicting binary outcomes based on the pair-copula construction," Empirical Economics, Springer, vol. 64(6), pages 3089-3119, June.
    2. Nagler, Thomas & Czado, Claudia, 2016. "Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 69-89.
    3. Brechmann, Eike C. & Hendrich, Katharina & Czado, Claudia, 2013. "Conditional copula simulation for systemic risk stress testing," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 722-732.
    4. Karoline Bax & Ozge Sahin & Claudia Czado & Sandra Paterlini, 2021. "ESG, Risk, and (Tail) Dependence," Papers 2105.07248, arXiv.org, revised Nov 2021.
    5. Zhu, Kailun & Kurowicka, Dorota & Nane, Gabriela F., 2021. "Simplified R-vine based forward regression," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    6. Derumigny Alexis & Fermanian Jean-David, 2017. "About tests of the “simplifying” assumption for conditional copulas," Dependence Modeling, De Gruyter, vol. 5(1), pages 154-197, August.
    7. Genest Christian & Scherer Matthias, 2019. "The world of vines: An interview with Claudia Czado," Dependence Modeling, De Gruyter, vol. 7(1), pages 169-180, January.
    8. Müller, Dominik & Czado, Claudia, 2019. "Dependence modelling in ultra high dimensions with vine copulas and the Graphical Lasso," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 211-232.
    9. Yousaf Ali Khan, 2022. "Modeling Dependent Structure Among Micro-Economics Variables Through COPAR (1)-Model in Pakistan," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 257-279, March.
    10. Kjersti Aas, 2016. "Pair-Copula Constructions for Financial Applications: A Review," Econometrics, MDPI, vol. 4(4), pages 1-15, October.
    11. Stöber, Jakob & Czado, Claudia, 2014. "Regime switches in the dependence structure of multidimensional financial data," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 672-686.
    12. Chang, Bo & Joe, Harry, 2019. "Prediction based on conditional distributions of vine copulas," Computational Statistics & Data Analysis, Elsevier, vol. 139(C), pages 45-63.
    13. Koliai, Lyes, 2016. "Extreme risk modeling: An EVT–pair-copulas approach for financial stress tests," Journal of Banking & Finance, Elsevier, vol. 70(C), pages 1-22.
    14. Levi, Evgeny & Craiu, Radu V., 2018. "Bayesian inference for conditional copulas using Gaussian Process single index models," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 115-134.
    15. Dalla Valle, Luciana & De Giuli, Maria Elena & Tarantola, Claudia & Manelli, Claudio, 2016. "Default probability estimation via pair copula constructions," European Journal of Operational Research, Elsevier, vol. 249(1), pages 298-311.
    16. Holger Fink & Yulia Klimova & Claudia Czado & Jakob Stober, 2016. "Regime switching vine copula models for global equity and volatility indices," Papers 1604.05598, arXiv.org.
    17. Wanling Huang & André Varella Mollick & Khoa Huu Nguyen, 2017. "Dynamic responses and tail-dependence among commodities, the US real interest rate and the dollar," Empirical Economics, Springer, vol. 53(3), pages 959-997, November.
    18. Hobæk Haff, Ingrid & Aas, Kjersti & Frigessi, Arnoldo & Lacal, Virginia, 2016. "Structure learning in Bayesian Networks using regular vines," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 186-208.
    19. 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.
    20. Gijbels, Irène & Omelka, Marek & Pešta, Michal & Veraverbeke, Noël, 2017. "Score tests for covariate effects in conditional copulas," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 111-133.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:172:y:2022:i:c:s016794732200041x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.