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Estimation of Copula Models for Time Series of Possibly Different Length

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Author Info
Andrew Patton (University of Oxford)

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Abstract

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 2001-17.

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Date of creation: 12 Nov 2001
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Handle: RePEc:cdl:ucsdec:2001-17

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Related research
Keywords: copulas; maximum likelihood; two-stage estimation; exchange rates; missing data;

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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.:
  1. 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.
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    Other versions:
  3. Paul Kofman & Ian Sharpe, 2000. "Imputation Methods for Incomplete Dependent Variables in Finance," Econometric Society World Congress 2000 Contributed Papers 0409, Econometric Society. [Downloadable!]
  4. Gourieroux Christian & Monfort Alain & Trognon A, 1981. "Pseudo maximum likelihood methods : theory," CEPREMAP Working Papers (Couverture Orange) 8129, CEPREMAP.
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  5. 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. [Downloadable!]
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  6. Goetzmann, William N. & Jorion, Philippe, 1999. "Re-Emerging Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(01), pages 1-32, March. [Downloadable!]
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  7. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," Journal of Business, University of Chicago Press, vol. 36, pages 394. [Downloadable!]
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  9. Andrew J. Patton, 2004. "On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 130-168. [Downloadable!] (restricted)
  10. Stambaugh, Robert F., 1997. "Analyzing investments whose histories differ in length," Journal of Financial Economics, Elsevier, vol. 45(3), pages 285-331, September. [Downloadable!] (restricted)
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  11. Andrew J. Patton, 2001. "Modelling Time-Varying Exchange Rate Dependence Using the Conditional Copula," University of California at San Diego, Economics Working Paper Series 2001-09, Department of Economics, UC San Diego. [Downloadable!]
  12. 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-. [Downloadable!]
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  16. Tim Bollerslev & Jeffrey Wooldridge, 1992. "Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances," Econometric Reviews, Taylor and Francis Journals, vol. 11(2), pages 143-172. [Downloadable!] (restricted)
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    Other versions:
  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. 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. [Downloadable!]
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Full references

Cited by:
(explanations, 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.)

  1. Xiaohong Chen & Yanqin Fan, 2002. "Estimation of Copula-Based Semiparametric Time Series Models," Working Papers 0226, Department of Economics, Vanderbilt University, revised Oct 2004. [Downloadable!]
  2. Hong-Ming Huang & Chihwa Kao & Giovanni Urga, 2007. "Copula-Based Tests for Cross-Sectional Independence in Panel Models," Center for Policy Research Working Papers 99, Center for Policy Research, Maxwell School, Syracuse University. [Downloadable!]
    Other versions:
  3. Jian Hu, 2008. "Dependence Structures in Chinese and U.S. Financial Markets: A Time-varying Conditional Copula Approach," Departmental Working Papers 0808, Southern Methodist University, Department of Economics, revised Nov 2008. [Downloadable!]
    Other versions:
  4. Söehnke Bartram & Stephen Taylor & Yaw-Huei Wang, 2004. "The Euro and European Financial Market Integration," Money Macro and Finance (MMF) Research Group Conference 2004 49, Money Macro and Finance Research Group, revised 13 Oct 2004. [Downloadable!]
  5. Clive Granger & Timo Teräsvirta & Andrew Patton, 2002. "Common Factors in Conditional Distributions," University of California at San Diego, Economics Working Paper Series 2002-19, Department of Economics, UC San Diego. [Downloadable!]
    Other versions:
  6. Yanqin Fan & Xiaohong Chen, 2004. "Estimation of Copula-Based Semiparametric Time Series Models," Econometric Society 2004 Far Eastern Meetings 559, Econometric Society. [Downloadable!]
  7. Abel Elizalde, 2006. "Credit Risk Models I: Default Correlation In Intensity Models," Working Papers wp2006_0605, CEMFI. [Downloadable!]
  8. Jian Hu, 2008. "Does Weather Matter?," Departmental Working Papers 0809, Southern Methodist University, Department of Economics. [Downloadable!]
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