A copula test space model how to avoid the wrong copula choice

Michiels, Frederik   ; De Schepper, Ann

Kybernetika, Tome 44 (2008) no. 6, pp. 864-878

Abstract (VO)

We introduce and discuss the test space problem as a part of the whole copula fitting process. In particular, we explain how an efficient copula test space can be constructed by taking into account information about the existing dependence, and we present a complete overview of bivariate test spaces for all possible situations. The practical use will be illustrated by means of a numerical application based on an illustrative portfolio containing the S 500 Composite Index, the JP Morgan Government Bond Index and the NAREIT All index.

Détail

Classification : 62H12, 62H20, 62P05
Keywords: copula; Kendall’s tau; goodness-of-fit; copula test space; associated copulas

Bibliographie

[1] Aas K.: Modeling the dependence structure of financial assets: A survey of four copulas. Working paper Norwegian computing centre, SAMBA/22/044 (2004)

[2] Aas K., Czado C., Frigessi, A., Bakken H.: Pair-copula constructions of multiple dependence. Insurance: Mathematics and Economics. In press, 2007, doi:10.1016/j.insmatheco.2007.02.001 | Zbl

[3] Abid F., Naifar N.: The impact of stock returns volatility on credit default swap rates: A copula study (2005), available at SSRN: http:--ssrn</b> com/abstract=726726 MR 2192421

[4] Alsina C., Frank M. J., Schweizer B.: Associative Functions. World Scientific, Singapore 2006 | MR | Zbl

[5] Andersen P. K., Ekstrom C. T., Klein J. P., Shu, Y., Zhang M.: A class of goodness of fit tests for a copula base on bivariate right-censored data. Biometrical J. 47 (2005), 6, 815–826 | DOI | MR

[6] Ané T., Kharoubi C.: Dependence structure and risk measure. J. Business 76 (2003), 3, 441–438

[7] Bacigal T., Komorníková M.: Fitting Archimedean copulas to bivariate geodetic data. In: Proc. COMPSTAT, 2006, pp. 649–656

[8] Berg D., Aas K.: Models for construction of multivariate dependence: A comparison study (2007). Unpublished paper, available at http://www.danielberg.no/publications/highdim.pdf

[9] Bouyé E., Durrleman V., Nikeghbali A., Riboulet, G., Roncalli T.: Copulas for finance: A reading guide and some applications. Working paper Groupe de recherche Opérationelle Crédit Lyonnais 2000

[10] Cherubini U., Luciano, E., Vecchiato W.: Copula Methods in Finance. Wiley, New York 2004 | MR | Zbl

[11] Clemen R. T., Reilly T.: Correlations and copulas for decision and risk analysis. Management Sci. 45 (1999), 208–224 | DOI | Zbl

[12] Matteis R. De: Fitting Copulas to Data. Diploma Thesis, 2001

[13] Denuit M., Scaillet O.: Non-parametric tests for positive quadrant dependence. J. Financial Econometrics 2 (2004), 3, 422–450 | DOI

[14] Dobric J., Schmid F.: Testing goodness of fit for parametric families of copulas-application to financial data. Commun. Statist.: Simulation and Computation 34 (2005), 4, 1053–1068 | DOI | MR | Zbl

[15] Dobric J., Schmid F.: A goodness of fit test for copulas based on Rosenblatt’s transform. Comput. Statis. Data Anal. 51 (2007), 4633–4642 | DOI | MR

[16] Durrleman V., Nikeghbali, A., Roncalli T.: Which copula is the right one? Working paper Groupe de recherche Opérationelle Crédit Lyonnais 200.

[17] Fang H., Fang, K., Kotz S.: The meta-elliptical distributions with given marginals. J. Multivariate Anal. 82 (2002), 1–16 | DOI | MR | Zbl

[18] Fermanian J. D.: Goodness of fit tests for copulas. J. Multivariate Anal. 95 (2005), 1, 119–152 | DOI | MR | Zbl

[19] Frees E. W., Valdez E. A.: Understanding relationships using copulas. North American Actuarial J. 2 (1998), 1, 1–25 | DOI | MR | Zbl

[20] Genest C., Favre A.: Everything you always wanted to know about copula modeling but were afraid to ask. J. Hydrologic Engrg. 12 (2007), 4, 347–368 | DOI

[21] Genest C., Rivest L.: Statistical inference procedures for bivariate Archimedean copulas. J. Amer. Statist. Assoc. 88 (1993), 1034–1043 | DOI | MR | Zbl

[22] Genest C., MacKay R. J.: Copules archimédiennes et familles de lois bidimensionnelles dont les marges sont données. Canad. J. Statist. 14 (1986), 2, 145–159 | DOI | MR | Zbl

[24] Hofert M.: Sampling Archimedean copulas. Comput. Statist. Data Anal. 52 (2008), 12, 5163–5174 | DOI | MR

[25] Joe H.: Multivariate concordance. J. Multivariate Anal. 35 (1990), 12–30 | DOI | MR | Zbl

[26] Joe H.: Multivariate Models and Dependence Concepts. Chapman and Hall, London 1997 | MR | Zbl

[27] Klement E. P., Mesiar, R., Pap E.: Invariant copulas. Kybernetika 38 (2002), 275–285 | MR

[28] Kole E., Koedijk K. C. G., Verbeek M.: Selecting copulas for risk management. J. Banking and Finance 31 (2007), 2405–2423 | DOI

[29] Lindskog F., McNeil A. J., Schmock U.: Kendall’s tau for Elliptical Distributions. Technical Report, Risklab, ETH Zürich 2001

[30] McNeil A. J.: Sampling Archimedean copulas. J. Statist. Comput. Simul. 78 (2008), 6, 567–581 | DOI | MR

[31] Nelsen R. B.: Some concepts of bivariate symmetry. J. Nonparametric Statist. 3 (1993), 95–101 | DOI | MR

[32] Nelsen R. B.: Nonparametric measures of multivariate Aassociation. In: Distributions with Fixed Marginals and Related Topics 1996, pp. 223–232 | MR

[33] Nelsen R. B.: An Introduction to Copulas. Second edition. Springer-Verlag, New York 2006 | MR | Zbl

[34] Savu C., Trede M.: Goodness-of-fit tests for parametric families of Archimedean copulas. Quantitative Finance 8 (2008), 2, 109–116 | DOI | MR | Zbl

[35] Sklar A.: Fonctions de repartition $\grave{a}$ $n$ dimensions et leur marges. Publ. Inst. Statist. Univ. Paris 8 (1959), 229–231 | MR

[36] Smith M. D.: Modelling sample selection using Archimedean copulas. The Econometrics Journal 6 (2003), 1, 99–123 | DOI | MR | Zbl