Abstract
In econometrics, many distributions are non-Gaussian. To describe dependence between non-Gaussian variables, it is usually not sufficient to provide their correlation: it is desirable to also know the corresponding copula. There are many different families of copulas; which family shall we use? In many econometric applications, two families of copulas have been most efficient: the Clayton and the Gumbel copulas. In this paper, we provide a theoretical explanation for this empirical efficiency, by showing that these copulas naturally follow from reasonable symmetry assumptions. This symmetry justification also allows us to provide recommendations about which families of copulas we should use when we need a more accurate description of dependence.
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References
Berger, J.O.: Statistical Decision Theory and Bayesian Analysis. Springer, New York (2010)
Feynman, R., Leighton, R., Sands, M.: The Feynman Lectures on Physics. Addison Wesley, Boston (2005)
Finkelstein, A.M., Kreinovich, V., Zapatrin, R.R.: Fundamental physical equations uniquely determined by their symmetry groups. Springer Lecture Notes in Mathematics, vol. 1214, pp. 159–170. Springer, Heidelberg (1986)
Jaworski, P., Durante, F., Härdle, W.K., Ruchlik, T. (eds.): Copula Theory and Its Applications. Springer, Heidelberg (2010)
McNeil, A.J., Frey, R., Embrechts, P.: Quantitative Risk Management: Concepts, Techniques, Tools. Princeton University Press, Princeton (2005)
Nelsen, R.B.: An Introduction to Copulas. Springer, Heidelberg (1999)
Nguyen, H.T., Kreinovich, V.: Applications of Continuous Mathematics to Computer Science. Kluwer, Dordrecht (1997)
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Kreinovich, V., Nguyen, H.T., Sriboonchitta, S. (2013). Why Clayton and Gumbel Copulas: A Symmetry-Based Explanation. In: Huynh, VN., Kreinovich, V., Sriboonchitta, S., Suriya, K. (eds) Uncertainty Analysis in Econometrics with Applications. Advances in Intelligent Systems and Computing, vol 200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35443-4_6
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DOI: https://doi.org/10.1007/978-3-642-35443-4_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35442-7
Online ISBN: 978-3-642-35443-4
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