Estimation and Model Selection of Copulas with an Application to Exchange Rates
AbstractCopulas are the part of a multivariate distribution function that fully captures the cross sectional dependence between the variables of interest and they have become a very popular tool to model dependencies different from the linear correlation of elliptical distributions. We review the theory of copula functions, present a number of examples and describe how to sample random data from these. Different techniques for estimation and model selection are discussed and compared in an extensive Monte Carlo study. We find that a test not considered in the literature, namely the Jarque-Bera test applied on transformed data from the conditional copula, has the best properties of the presented tests, but that the most reliable criterion for selecting the best fitting copula is the Akaike information criterion. We model exchange rate returns of Latin American currencies against the euro with copulas and we find evidence of symmetric dependence, excess upper tail dependence and excess lower tail dependence.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 056.
Date of creation: 2007
Date of revision:
Contact details of provider:
Web page: http://www.maastrichtuniversity.nl/web/UMPublications.htm
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-02-02 (All new papers)
- NEP-ECM-2008-02-02 (Econometrics)
- NEP-IFN-2008-02-02 (International Finance)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Markus Junker & Angelika May, 2005. "Measurement of aggregate risk with copulas," Econometrics Journal, Royal Economic Society, vol. 8(3), pages 428-454, December.
- Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, .
"Evaluating Density Forecasts,"
CARESS Working Papres
97-18, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
- Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, 1997. "Evaluating Density Forecasts," NBER Technical Working Papers 0215, National Bureau of Economic Research, Inc.
- Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, 1997. "Evaluating density forecasts," Working Papers 97-6, Federal Reserve Bank of Philadelphia.
- Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, 1997. "Evaluating Density Forecasts," Center for Financial Institutions Working Papers 97-37, Wharton School Center for Financial Institutions, University of Pennsylvania.
- Markus Junker & Alexander Szimayer & Niklas Wagner, 2004. "Nonlinear Term Structure Dependence: Copula Functions, Empirics, and Risk Implications," Econometrics 0401007, EconWPA.
- Goorbergh, R.W.J. van den & Genest, C. & Werker, B.J.M., 2003. "Multivariate Option Pricing Using Dynamic Copula Models," Discussion Paper 2003-122, Tilburg University, Center for Economic Research.
- Chen, Xiaohong & Fan, Yanqin & Tsyrennikov, Viktor, 2006.
"Efficient Estimation of Semiparametric Multivariate Copula Models,"
Journal of the American Statistical Association,
American Statistical Association, vol. 101, pages 1228-1240, September.
- Xiaohong Chen & Yanqin Fan & Victor Tsyrennifov, 2004. "Efficient Estimation of Semiparametric Multivariate Copula Models," Vanderbilt University Department of Economics Working Papers 0420, Vanderbilt University Department of Economics.
- Granger, Clive W.J. & Teräsvirta, Timo & Patton, Andrew J., 2002.
"Common factors in conditional distributions,"
Working Paper Series in Economics and Finance
515, Stockholm School of Economics.
- Granger, Clive W.J. & TerÃ¤svirta, Timo & Patton, Andrew J, 2002. "Common Factors in Conditional Distributions," University of California at San Diego, Economics Working Paper Series qt3bd1n1x5, Department of Economics, UC San Diego.
- Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-74, October.
- Andrew J. Patton, 2006. "Estimation of multivariate models for time series of possibly different lengths," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(2), pages 147-173.
- Thierry Roncalli & Gael Riboulet & Ashkan Nikeghbali & Vado Durrleman & Erick Bouy?, 2001. "Copulas: an Open Field for Risk Management," Working Papers wp01-01, Warwick Business School, Finance Group.
- Junker, Markus & Szimayer, Alex & Wagner, Niklas, 2006. "Nonlinear term structure dependence: Copula functions, empirics, and risk implications," Journal of Banking & Finance, Elsevier, vol. 30(4), pages 1171-1199, April.
- Andrew Patton, 2004.
"Modelling Asymmetric Exchange Rate Dependence,"
wp04-04, Warwick Business School, Finance Group.
- repec:cup:cbooks:9780521496032 is not listed on IDEAS
- Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July.
- Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 125-154.
- Andrew J. Patton, 2004. "On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 130-168.
- Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
- Boubaker, Heni & Sghaier, Nadia, 2013. "Portfolio optimization in the presence of dependent financial returns with long memory: A copula based approach," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 361-377.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Charles Bollen).
If references are entirely missing, you can add them using this form.