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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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  1. 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.
  2. 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.
  3. 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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  14. Joshua V. Rosenberg, 2003. "Nonparametric pricing of multivariate contingent claims," Staff Reports 162, Federal Reserve Bank of New York.
  15. ROCKINGER, Michael & JONDEAU, Eric, 2001. "Conditional dependency of financial series : an application of copulas," Les Cahiers de Recherche 723, HEC Paris.
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  17. 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.
  18. 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.
  19. 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-.
  20. Gourieroux Christian & Monfort Alain & Trognon A, 1981. "Pseudo maximum likelihood methods : theory," CEPREMAP Working Papers (Couverture Orange) 8129, CEPREMAP.
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