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Estimation of Copula Models for Time Series of Possibly Different Length

  • Patton, Andrew J

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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Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number qt3fc1c8hw.

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Date of creation: 12 Nov 2001
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Handle: RePEc:cdl:ucsdec:qt3fc1c8hw
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  11. 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.
  12. 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.
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  15. Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
  16. 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-.
  17. 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.
  18. Joshua V. Rosenberg, 2003. "Nonparametric pricing of multivariate contingent claims," Staff Reports 162, Federal Reserve Bank of New York.
  19. 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.
  20. Ang, Andrew & Chen, Joseph, 2002. "Asymmetric correlations of equity portfolios," Journal of Financial Economics, Elsevier, vol. 63(3), pages 443-494, March.
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