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Copulae in Mathematical and Quantitative Finance pp 17–37Cite as

Selection of Vine Copulas

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Part of the book series: Lecture Notes in Statistics ((LNSP,volume 213))

Abstract

Vine copula models have proven themselves as a very flexible class of multivariate copula models with regard to symmetry and tail dependence for pairs of variables. The full specification of a vine model requires the choice of a vine tree structure, the copula families for each pair copula term and their corresponding parameters. In this survey we discuss the different approaches, both frequentist and Bayesian, for these model choices so far and point to open problems.

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References

  1. Aas, K., Czado, C., Frigessi, A., Bakken, H.: Pair-copula constructions of multiple dependence. Insur. Math. Econ. 44, 182–198 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  2. Acar, E.F., Genest, C., Nešlehová, J.: Beyond simplified pair-copula constructions. J. Multivar. Anal. 110, 74–90 (2012)

    Article  MATH  Google Scholar 

  3. Almeida, C., Czado, C.: Efficient Bayesian inference for stochastic time-varying copula models. Comput. Stat. Data Anal. 56(6), 1511–1527 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  4. Almeida, C., Czado, C., Manner, H.: Modeling high dimensional time-varying dependence using D-vine SCAR models. http://arxiv.org/abs/1202.2008 (2012, preprint)

  5. Baba, K., Shibata, R., Sibuya, M.: Partial correlation and conditional correlation as measures of conditional independence. Aust. N. Z. J. Stat. 46(4), 657–664 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bauer, A., Czado, C.: Pair copula Bayesian networks. http://arxiv.org/abs/1211.5620 (2012, preprint)

  7. Bauer, A., Czado, C., Klein, T.: Pair-copula constructions for non-Gaussian DAG models. Can. J. Stat. 40(1), 86–109 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Bedford, T., Cooke, R.M.: Probability density decomposition for conditionally dependent random variables modeled by vines. Ann. Math. Artif. Intell. 32, 245–268 (2001)

    Article  MathSciNet  Google Scholar 

  9. Bedford, T., Cooke, R.M.: Vines: a new graphical model for dependent random variables. Ann. Stat. 30(4), 1031–1068 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  10. Berg, D., Aas, K.: Models for construction of higher-dimensional dependence: a comparison study. Eur. J. Financ. 15, 639–659 (2009)

    Article  Google Scholar 

  11. Brechmann, E.C.: Truncated and simplified regular vines and their applications. Master’s thesis, Technische Universität München (2010)

    Google Scholar 

  12. Brechmann, E.C., Czado, C.: Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50. Stat. Risk Model. (2013, in press)

    Google Scholar 

  13. Brechmann, E.C., Czado, C.: COPAR - Multivariate time series modeling using the COPula AutoRegressive model. http://arxiv.org/abs/1203.3328 (2012, preprint)

  14. Brechmann, E.C., Czado, C., Aas, K.: Truncated regular vines in high dimensions with application to financial data. Can. J. Stat. 40(1), 68–85 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  15. Brechmann, E.C., Schepsmeier, U.: Modeling dependence with C- and D-vine copulas: the R-package CDVine. J. Stat. Softw. 52(3), 1–27 (2012)

    Google Scholar 

  16. Brooks, S., Gelman, A., Jones, G.L., Meng, X.L.: Handbook of Markov Chain Monte Carlo. Chapman & Hall/CRC, Boca Raton (2011)

    Book  MATH  Google Scholar 

  17. Chollete, L., Heinen, A., Valdesogo, A.: Modeling international financial returns with a multivariate regime switching copula. J. Financ. Econom. 7, 437–480 (2009)

    Article  Google Scholar 

  18. Clarke, K.A.: A simple distribution-free test for nonnested model selection. Polit. Anal. 15(3), 347–363 (2007)

    Article  Google Scholar 

  19. Cormen, T., Leiserson, E., Rivest, R., Stein, C.: Introduction to Algorithms. The MIT Press, Cambridge (2009)

    MATH  Google Scholar 

  20. Czado, C.: Pair copula constructions of multivariate copulas. In: Jaworki, P., Durante, F., Härdle, W., Rychlik, W. (eds.) Workshop on Copula Theory and its Applications. Springer, Berlin (2010)

    Google Scholar 

  21. Czado, C., Jeske, S., Hofmann, M.: Selection strategies for regular vine copulae. (2012, preprint)

    Google Scholar 

  22. Czado, C., Schepsmeier, U., Min, A.: Maximum likelihood estimation of mixed C-vines with application to exchange rates. Stat. Modelling 12(3), 229–255 (2012)

    Article  Google Scholar 

  23. Dißmann, J., Brechmann, E.C., Czado, C., Kurowicka, D.: Selecting and estimating regular vine copulae and application to financial returns. Comput. Stat. Data Anal. 59(1), 52–69 (2013)

    Article  Google Scholar 

  24. Fischer, M., Köck, C., Schlüter, S., Weigert, F.: An empirical analysis of multivariate copula models. Quant. Financ. 9(7), 839–854 (2009)

    Article  MATH  Google Scholar 

  25. Genest, C., Ghoudi, K., Rivest, L.P.: A semiparametric estimation procedure of dependence parameters in multivariate families of distributions. Biometrika 82, 543–552 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  26. Genest, C., Werker, B.J.M.: Conditions for the asymptotic semiparametric efficiency of an omnibus estimator of dependence parameters in copula models. In: Cuadras, C.M., Fortiana, J., Rodríguez Lallena, J.A. (eds.) Distributions with Given Marginals and Statistical Modelling, pp. 103–112. Kluwer, Dordrecht (2002)

    Google Scholar 

  27. Green, P.J.: Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82, 711–732 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  28. Gruber, L.F.: Bayesian analysis of R-vine copulas. Master’s thesis. Technische Universität München (2011)

    Google Scholar 

  29. Gruber, L.F., Czado C.: Sequential Bayesian model selection of regular vine copulas. (2013, preprint)

    Google Scholar 

  30. Hanea, A., Kurowicka, D., Cooke, R.: Hybrid method for quantifying and analyzing Bayesian belief nets. Qual. Reliab. Eng. Int. 22(6), 613–729 (2006)

    Article  Google Scholar 

  31. Hastings, W.: Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97–109 (1970)

    Article  MATH  Google Scholar 

  32. Heinen, A., Valdesogo, A.: Asymmetric CAPM dependence for large dimensions: The Canonical Vine Autoregressive Model. CORE discussion papers 2009069. Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) (2009)

    Google Scholar 

  33. Hobæk Haff, I.: Parameter estimation for pair-copula constructions. Bernoulli 19(2), 462–491 (2013)

    Article  MATH  Google Scholar 

  34. Hobæk Haff, I.: Comparison of estimators for pair-copula constructions. J. Multivar. Anal. 110, 91–105 (2012)

    Article  MATH  Google Scholar 

  35. Hobæk Haff, I., Aas, K., Frigessi, A.: On the simplified pair-copula construction - simply useful or too simplistic? J. Multivar. Anal. 101(5), 1296–1310 (2010)

    Article  MATH  Google Scholar 

  36. Hobæk Haff, I., Segers, J.: Nonparametric estimation of pair-copula constructions with the empirical pair-copula. http://arxiv.org/abs/1201.5133 (2012, preprint)

  37. Joe, H.: Families of m-variate distributions with given margins and m(m − 1) ∕ 2 bivariate dependence parameters. In: Rüschendorf, L., Schweizer, B., Taylor, M.D. (eds.) Distributions with Fixed Marginals and Related Topics, pp. 120–141. Institute of Mathematical Statistics, Hayward (1996)

    Chapter  Google Scholar 

  38. Joe, H.: Asymptotic efficiency of the two-stage estimation method for copula-based models. J. Multivar. Anal. 94, 401–419 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  39. Joe, H., Xu, J.: The estimation method of inference functions for margins for multivariate models. Technical Report 166, Department of Statistics, University of British Columbia (1996)

    Google Scholar 

  40. Kojadinovic, I., Yan, J.: Modeling multivariate distributions with continuous margins using the copula R package. J. Stat. Softw. 34(9), 1–20 (2010)

    MathSciNet  Google Scholar 

  41. Kojadinovic, I., Yan, J.: A goodness-of-fit test for multivariate multiparameter copulas based on multiplier central limit theorems. Stat. Comput. 21, 17–30 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  42. Kojadinovic, I., Yan, J., Holmes, M.: Fast large-sample goodness-of-fit test for copulas. Statistica Sinica 21, 841–871 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  43. Kurowicka, D.: Optimal truncation of vines. In: Kurowicka, D., Joe, H. (eds.) Dependence Modeling: Vine Copula Handbook. World Scientific, Singapore (2011)

    Google Scholar 

  44. Kurowicka, D., Cooke, R.: Distribution-free continuous Bayesian belief nets. In: Wilson, A., Limnios, N., Keller-McNulty, S., Armojo, Y. (eds.) Modern Statistical and Mathematical Methods in Reliability, pp. 309–323. World Scientific, Singapore (2005)

    Chapter  Google Scholar 

  45. Kurowicka, D., Cooke, R.M.: Uncertainty Analysis with High Dimensional Dependence Modelling. Wiley, Chichester (2006)

    Book  MATH  Google Scholar 

  46. Kurowicka, D., Joe, H.: Dependence Modeling: Vine Copula Handbook. World Scientific, Singapore (2011)

    Google Scholar 

  47. Manner, H.: Estimation and model selection of copulas with an application to exchange rates. METEOR research memorandum 07/056. Maastricht University (2007)

    Google Scholar 

  48. Mendes, B.V.d.M., Semeraro, M.M., Leal, R.P.C.: Pair-copulas modeling in finance. Financ. Markets Portfolio Manag. 24(2), 193–213 (2010)

    Google Scholar 

  49. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equation of State Calculations by Fast Computing Machines. J. Chem. Phys. 21, 1087–1092 (1953)

    Article  Google Scholar 

  50. Meyn, S., Tweedie, R.L.: Markov Chain and Stochastic Stability, 2nd edn. Cambridge University Press, Cambridge (2009)

    Book  Google Scholar 

  51. Min, A., Czado, C.: Bayesian inference for multivariate copulas using pair-copula constructions. J. Financ. Econom. 8(4), 511–546 (2010)

    Google Scholar 

  52. Min, A., Czado, C.: Bayesian model selection for D-vine pair-copula constructions. Can. J. Stat. 39, 239–258 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  53. Morales-Nápoles, O.: Counting vines. In: Kurowicka, D., Joe, H. (eds.) Dependence Modeling: Vine Copula Handbook. World Scientific, Singapore (2011)

    Google Scholar 

  54. Nikoloulopoulos, A.K., Joe, H., Li, H.: Vine copulas with asymmetric tail dependence and applications to financial return data. Comput. Stat. Data Anal. 56(11), 3659–3673 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  55. Panagiotelis, A., Czado, C., Joe, H.: Pair copula constructions for multivariate discrete data. J. Am. Stat. Assoc. 107(499), 1063–1072 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  56. Schellhase, C., Kauermann, G.: Flexible pair-copula estimation in D-vines with penalized splines. (2012, preprint)

    Google Scholar 

  57. Schepsmeier, U., Brechmann, E.C.: CDVine: Statistical Inference of C- and D-Vine Copulas. R package version 1.1-12. http://CRAN.R-project.org/package=CDVine (2013)

  58. Schepsmeier, U., Stoeber, J., Brechmann, E.C.: VineCopula: Statistical Inference of Vine Copulas. R package version 1.1-1. http://CRAN.R-project.org/package=VineCopula (2013)

  59. Siek, J., Lee, L.Q., Lumsdaine, A.: Boost Graph Library: Random Spanning Tree - 1.49.0. http://www.boost.org/doc/libs/1_49_0/libs/graph/doc/random_spanning_tree.html (2012)

  60. Sklar, A.: Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8, 229–231 (1959)

    MathSciNet  Google Scholar 

  61. Smith, M., Min, A., Almeida, C., Czado, C.: Modeling Longitudinal Data Using a Pair-Copula Decomposition of Serial Dependence. J. Am. Stat. Assoc. 105(492), 1467–1479 (2010)

    Article  MathSciNet  Google Scholar 

  62. Stöber, J., Czado, C.: Detecting regime switches in the dependence structure of high dimensional financial data. http://arxiv.org/abs/1202.2009 (2011, preprint)

  63. Stöber, J., Czado, C., Hong, H., Ghosh, P.: Interrelation among chronic diseases in the elderly. (2012, preprint)

    Google Scholar 

  64. Stöber, J., Czado, C., Joe, H.: Simplified pair copula constructions - limits and extensions. http://arxiv.org/abs/1205.4844 (2012, preprint)

  65. Stöber, J., Schepsmeier, U.: Is there significant time-variation in multivariate copulas? http://arxiv.org/abs/1205.4841 (2012, preprint)

  66. Vuong, Q.H.: Ratio tests for model selection and non-nested hypotheses. Econometrica 57(2), 307–333 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  67. Whittaker, J.: Graphical Models in Applied Multivariate Statistics. Wiley, New York (1990)

    MATH  Google Scholar 

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Acknowledgements

The second and third author gratefully acknowledge the support of the TUM Graduate School’s International School of Applied Mathematics. The second author is also supported by a research stipend from Allianz Deutschland AG.

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Authors and Affiliations

  1. Zentrum Mathematik, Technische Universität München, Munich, Germany

    Claudia Czado, Eike Christian Brechmann & Lutz Gruber

Authors
  1. Claudia Czado
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  2. Eike Christian Brechmann
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  3. Lutz Gruber
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Corresponding author

Correspondence to Claudia Czado .

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Editors and Affiliations

  1. Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, ul. Banacha 2, Warszawa, 02097, Poland

    Piotr Jaworski

  2. School of Economics and Management, Free University of Bozen-Bolzano, Piazza Università 1, Bozen, 39100, Italy

    Fabrizio Durante

  3. L.v.Bortkiewicz Chair of Statistics, C.A.S.E. Centre f. Appl. Stat. & Econ., Humboldt-Universität zu Berlin, Unter den Linden 6, Berlin, 10099, Germany

    Wolfgang Karl Härdle

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Czado, C., Brechmann, E.C., Gruber, L. (2013). Selection of Vine Copulas. In: Jaworski, P., Durante, F., Härdle, W. (eds) Copulae in Mathematical and Quantitative Finance. Lecture Notes in Statistics(), vol 213. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35407-6_2

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