Estimation of Copula Models for Time Series of Possibly Different Length
The theory of conditional copulas provides a means of constructing flexible multivariate density models, allowing for time varying conditional densities of each individual variable, and for time-varying conditional dependence between the variables. Further, the use of copulas in constructing these models often allows for the partitioning of the parameter vector into elements relating only to a marginal distribution, and elements relating to the copula. This paper presents a two-stage (or multi-stage) maximum likelihood estimator for the case that such a partition is possible. We extend the existing statistics literature on the estimation of copula models to consider data that exhibit temporal dependence and heterogeneity. The estimator is flexible enough that the case that unequal amounts of data are available on each variable is easily handled. We investigate the small sample properties of the estimator in a Monte Carlo study, and find that it performs well in comparisons with the standard (one-stage) maximum likelihood estimator. Finally, we present an application of the estimator to a model of the joint distribution of daily Japanese yen - U.S. dollar and euro - U.S. dollar exchange rates. We find some evidence that a copula that captures asymmetric dependence performs better than those that assume symmetric dependence.
|Date of creation:||12 Nov 2001|
|Date of revision:|
|Contact details of provider:|| Postal: 9500 Gilman Drive, La Jolla, CA 92093-0508|
Phone: (858) 534-3383
Fax: (858) 534-7040
Web page: http://www.escholarship.org/repec/ucsdecon/
More information through EDIRC
References listed on IDEAS
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.:
- Paul Kofman & Ian Sharpe, 2000. "Imputation Methods for Incomplete Dependent Variables in Finance," Research Paper Series 33, Quantitative Finance Research Centre, University of Technology, Sydney.
- Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984.
"Pseudo Maximum Likelihood Methods: Theory,"
Econometric Society, vol. 52(3), pages 681-700, May.
- Paul Kofman & Ian Sharpe, 2000. "Imputation Methods for Incomplete Dependent Variables in Finance," Econometric Society World Congress 2000 Contributed Papers 0409, Econometric Society.
- Joshua Rosenberg, 1999. "Semiparametric Pricing of Multivariate Contingent Claims," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-028, New York University, Leonard N. Stern School of Business-.
- William Goetzmann & Philippe Jorion, 1998.
Yale School of Management Working Papers
ysm50, Yale School of Management, revised 01 Aug 2000.
- Kee-Hong Bae & G. Andrew Karolyi & Rene M. Stulz, 2001.
"A new approach to measuring financial contagion,"
743, Federal Reserve Bank of Chicago.
- François Longin, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, 04.
- Benoit Mandelbrot, 1963.
"The Variation of Certain Speculative Prices,"
The Journal of Business,
University of Chicago Press, vol. 36, pages 394.
- Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-83, November.
- Farebrother, R. W., 1992. "A Class of Bivariate Density Functions with Common Marginals," Econometric Theory, Cambridge University Press, vol. 8(01), pages 145-146, March.
- Rockinger, M. & Jondeau, E., 2001.
"Conditional Dependency of Financial Series: An Application of Copulas,"
82, Banque de France.
- Michael Rockinger & Eric Jondeau, 2001. "Conditional Dependency of Financial Series: An Application of Copulas," Working Papers hal-00601478, HAL.
- ROCKINGER, Michael & JONDEAU, Eric, 2001. "Conditional dependency of financial series : an application of copulas," Les Cahiers de Recherche 723, HEC Paris.
- Andrews, Donald W. K., 1987.
"Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables,"
645, California Institute of Technology, Division of the Humanities and Social Sciences.
- Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(03), pages 458-467, December.
- Asger Lunde & Peter R. Hansen, 2005.
"A forecast comparison of volatility models: does anything beat a GARCH(1,1)?,"
Journal of Applied Econometrics,
John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
- Asger Lunde & Peter Reinhard Hansen, 2001. "A Forecast Comparison of Volatility Models: Does Anything Beat a GARCH(1,1)?," Working Papers 2001-04, Brown University, Department of Economics.
- Farebrother, R.W., 1993. "A Class of Bivariate Density Functions with Common Marginals," Econometric Theory, Cambridge University Press, vol. 9(01), pages 148-149, January.
- Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
- Newey, Whitney K., 1987.
"Asymptotic Properties of One-Step Estimator Obtained from an Optimal Step Size,"
Cambridge University Press, vol. 3(02), pages 305-306, April.
- Newey, Whitney K., 1988. "Asymptotic Properties of One-step Estimator Obtained from an Optimal Step-size," Econometric Theory, Cambridge University Press, vol. 4(02), pages 359-361, August.
- Joshua V. Rosenberg, 2003. "Nonparametric pricing of multivariate contingent claims," Staff Reports 162, Federal Reserve Bank of New York.
- Jean-David FERMANIAN & Olivier SCAILLET, 2003. "Nonparametric Estimation of Copulas for Time Series," FAME Research Paper Series rp57, International Center for Financial Asset Management and Engineering.
- Ang, Andrew & Chen, Joseph, 2002. "Asymmetric correlations of equity portfolios," Journal of Financial Economics, Elsevier, vol. 63(3), pages 443-494, March.
- Patton, Andrew J, 2001. "Modelling Time-Varying Exchange Rate Dependence Using the Conditional Copula," University of California at San Diego, Economics Working Paper Series qt01q7j1s2, Department of Economics, UC San Diego.
When requesting a correction, please mention this item's handle: RePEc:cdl:ucsdec:qt3fc1c8hw. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Lisa Schiff)
If references are entirely missing, you can add them using this form.