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.
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- 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 863-883, November.
- Goetzmann, William N. & Jorion, Philippe, 1999.
Journal of Financial and Quantitative Analysis,
Cambridge University Press, vol. 34(01), pages 1-32, March.
- William N. Goetzmann & Philippe Jorion, 1997. "Re-emerging Markets," NBER Working Papers 5906, National Bureau of Economic Research, Inc.
- William Goetzmann & Philippe Jorion, 1998. "Re-emerging Markets," Yale School of Management Working Papers ysm50, Yale School of Management, revised 01 Aug 2000.
- Philippe Jorion & William N. Goetzmann, 1998. "Re-Emerging Markets," Yale School of Management Working Papers ysm111, Yale School of Management.
- Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
- Gourieroux Christian & Monfort Alain & Trognon A, 1981. "Pseudo maximum likelihood methods : theory," CEPREMAP Working Papers (Couverture Orange) 8129, CEPREMAP.
- Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
- 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., 1992. "A Class of Bivariate Density Functions with Common Marginals," Econometric Theory, Cambridge University Press, vol. 8(01), pages 145-146, March.
- 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-.
- François Longin, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, 04.
- Michael Rockinger & Eric Jondeau, 2001. "Conditional Dependency of Financial Series: An Application of Copulas," Working Papers hal-00601478, HAL.
- Rockinger, M. & Jondeau, E., 2001. "Conditional Dependency of Financial Series: An Application of Copulas," Working papers 82, Banque de France.
- ROCKINGER, Michael & JONDEAU, Eric, 2001. "Conditional dependency of financial series : an application of copulas," Les Cahiers de Recherche 723, HEC Paris.
- Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394-394.
- 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.
- Newey, Whitney K., 1987. "Asymptotic Properties of One-Step Estimator Obtained from an Optimal Step Size," Econometric Theory, Cambridge University Press, vol. 3(02), pages 305-306, April.
- Joshua V. Rosenberg, 2003. "Nonparametric pricing of multivariate contingent claims," Staff Reports 162, Federal Reserve Bank of New York.
- 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.
- Paul Kofman & Ian Sharpe, 2000. "Imputation Methods for Incomplete Dependent Variables in Finance," Econometric Society World Congress 2000 Contributed Papers 0409, Econometric Society.
- Kee-Hong Bae & G. Andrew Karolyi & René M. Stulz, 2003. "A New Approach to Measuring Financial Contagion," Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 717-763, July.
- Kee-Hong Bae & G. Andrew Karolyi & Rene M. Stulz, 2000. "A New Approach to Measuring Financial Contagion," NBER Working Papers 7913, National Bureau of Economic Research, Inc.
- Kee-Hong Bae & G. Andrew Karolyi & Rene M. Stulz, 2001. "A new approach to measuring financial contagion," Proceedings 743, Federal Reserve Bank of Chicago.
- Ang, Andrew & Chen, Joseph, 2002. "Asymmetric correlations of equity portfolios," Journal of Financial Economics, Elsevier, vol. 63(3), pages 443-494, March.
- 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.
- 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.
- Andrews, Donald W. K., 1987. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Working Papers 645, California Institute of Technology, Division of the Humanities and Social Sciences.
- 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.
- 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. Full references (including those not matched with items on IDEAS)