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Estimation of Copula Models for Time Series of Possibly Different Length

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  • Patton, Andrew J

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.

Suggested Citation

  • Patton, Andrew J, 2001. "Estimation of Copula Models for Time Series of Possibly Different Length," University of California at San Diego, Economics Working Paper Series qt3fc1c8hw, Department of Economics, UC San Diego.
  • Handle: RePEc:cdl:ucsdec:qt3fc1c8hw
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Andrew Patton, 2002. "(IAM Series No 001) On the Out-Of-Sample Importance of Skewness and Asymetric Dependence for Asset Allocation," FMG Discussion Papers dp431, Financial Markets Group.
    2. repec:wsi:jfexxx:v:02:y:2015:i:01:n:s2345768615500087 is not listed on IDEAS
    3. Granger, Clive W.J. & Teräsvirta, Timo & Patton, Andrew J., 2002. "Common factors in conditional distributions," SSE/EFI Working Paper Series in Economics and Finance 515, Stockholm School of Economics.
    4. Morettin Pedro A. & Toloi Clelia M.C. & Chiann Chang & de Miranda José C.S., 2011. "Wavelet Estimation of Copulas for Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 3(3), pages 1-31, October.
    5. Granger, Clive W.J. & Terasvirta, Timo & Patton, Andrew J., 2006. "Common factors in conditional distributions for bivariate time series," Journal of Econometrics, Elsevier, vol. 132(1), pages 43-57, May.
    6. repec:wsi:ijtafx:v:15:y:2012:i:03:n:s0219024912500197 is not listed on IDEAS
    7. Y. Malevergne & D. Sornette, 2003. "Testing the Gaussian copula hypothesis for financial assets dependences," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 231-250.
    8. Y. Malevergne & D. Sornette, 2002. "Investigating Extreme Dependences: Concepts and Tools," Papers cond-mat/0203166, arXiv.org.
    9. 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.
    10. Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July.
    11. Y. Malevergne & D. Sornette, 2002. "Tail Dependence of Factor Models," Papers cond-mat/0202356, arXiv.org.

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