Kybernetika 49 no. 3, 487-497, 2013

Modelling financial time series using reflections of copulas

Jozef Komorník and Magda Komorníková


We have intensified studies of reflections of copulas (that we introduced recently in \cite{Kom}) and found that their convex combinations exhibit potentially useful fitting properties for original copulas of the Normal, Frank, Clayton and Gumbel types. We show that these properties enable us to construct interesting models for the relations between investment in stocks and gold.


copula, tail dependence, survival copula, reflections of copulas, stock index, returns of index investments, returns of gold investments


93E12, 62A10


  1. D. Berg and H. Bakken: Copula goodness-of-fit tests: A comparative study. Working Paper, University of Oslo and Norwegian Computing Center 2006.   CrossRef
  2. J. Dobrič and F. Schmid: Testing goodness of fit for parametric families of copulas - Application to financial data. In: Comm. Statist. - Simulation Comput. 34 (2005), 1053-1068.   CrossRef
  3. P. Embrechts, F. Lindskog and A. McNail: Modeling dependence with copulas and applications to risk management. In: Handbook of Heavy Tailed Distributions in Finance (S. Rachev, ed.), Elsevier, Chapter 8, (2001), pp. 329-384.   CrossRef
  4. C. Genest and A. C. Favre: Everything you always wanted to know about copula modeling but were afraid to ask. J. Hydrologic Engrg. 12 (2007), 4, 347-368.   CrossRef
  5. H. Joe: Models and Dependence Concepts. Chapman and Hall, London 1997.   CrossRef
  6. J. Komorník and M. Komorníková: Reflections of copulas and their applications in modelling of financial data. Forum Statisticum Slovacum 1, (2012), 12-19.   CrossRef
  7. R. B. Nelsen: An introduction to copulas. In: Lecture Notes in Statist. 139, Springer-Verlag, New York 1999.   CrossRef
  8. C. Ning: Extreme dependence of international stock market. Working Paper, Ryerson University, 2008.   CrossRef
  9. C. Ning: Dependence structure between the equity market and the foreign exchange market - a copula approach. J. Internat. Money and Finance 29 (2010), 5, 743-759.   CrossRef
  10. A. J. Patton: Modelling asymmetric exchange rate dependence. Internat. Econom. Rev. 47 (2006), 2, 527-556.   CrossRef