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5 - Asymmetric Copulas

High Dimension

from Part One - Theory

Published online by Cambridge University Press:  03 January 2019

Lan Zhang
Affiliation:
Texas A & M University
V. P. Singh
Affiliation:
Texas A & M University
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Summary

Much of the literature on copulas, discussed in the previous chapters, is limited to the bivariate cases. The Gaussian and student copulas have been commonly applied to model the dependence in higher dimensions (Genest and Favre, 2007; Genest et al., 2007a). In Chapter 4, we discussed the extension of symmetric bivariate Archimedean copulas as well as their major restrictions to model high-dimensional dependence (i.e., d ≥ 3)d≥3). Through the extension of the bivariate Archimedean copula, the multivariate Archimedean copula is symmetric and denoted as exchangeable Archimedean copula (EAC). EAC allows for the specification of only one generating function and only one set of parameters θ. In other words, random variates by pair share the same degree of dependence. Using the trivariate random variable {X1, X2, X3} as an example, {X1, X2}, {X2, X3}, and {X1, X3} should have the same degree of dependence. However, this assumption is rarely valid. This chapter discusses the following two approaches of constructing asymmetric multivariate copulas: nested Archimedean copula construction (NAC) and the vine copulas through pair-copula construction (PCC).

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Publisher: Cambridge University Press
Print publication year: 2019

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References

References

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Additional Reading

Francesco, S. and Salvatore, G. (2007). Fully nested 3-copula: procedure and application on hydrological data. Journal of Hydrologic Engineering, 12(4), 420430.Google Scholar
Salvatori, G. and Francesco, S. (2006). Asymmetric copula in multivariate flood frequency analysis. Advanced in Water Resources, 29, 11551167.Google Scholar
Salvadori, G., De Michele, C., Kottegoda, N., and Rosso, R. (2007). Extremes in Nature: An Approach Using Copulas. Water Science and Technology Library, Vol. 56, Springer, Dordrecht.Google Scholar
Salvadori, G. and De Michele, C. (2007), On the use of copulas in hydrology: theory and practice. Journal of Hydrologic Engineering, 12(4), 369380.Google Scholar

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  • Asymmetric Copulas
  • Lan Zhang, Texas A & M University, V. P. Singh, Texas A & M University
  • Book: Copulas and their Applications in Water Resources Engineering
  • Online publication: 03 January 2019
  • Chapter DOI: https://doi.org/10.1017/9781108565103.006
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  • Asymmetric Copulas
  • Lan Zhang, Texas A & M University, V. P. Singh, Texas A & M University
  • Book: Copulas and their Applications in Water Resources Engineering
  • Online publication: 03 January 2019
  • Chapter DOI: https://doi.org/10.1017/9781108565103.006
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Asymmetric Copulas
  • Lan Zhang, Texas A & M University, V. P. Singh, Texas A & M University
  • Book: Copulas and their Applications in Water Resources Engineering
  • Online publication: 03 January 2019
  • Chapter DOI: https://doi.org/10.1017/9781108565103.006
Available formats
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