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Inhomogeneous dependency modelling with time varying copulae

Author

Listed:
  • Giacomini, Enzo
  • Härdle, Wolfgang Karl
  • Ignatieva, Ekaterina
  • Spokoiny, Vladimir

Abstract

Measuring dependence in a multivariate time series is tantamount to modelling its dynamic structure in space and time. In the context of a multivariate normally distributed time series, the evolution of the covariance (or correlation) matrix over time describes this dynamic. A wide variety of applications, though, requires a modelling framework different from the multivariate normal. In risk management the non-normal behaviour of most financial time series calls for nonlinear (i.e. non-gaussian) dependency. The correct modelling of non-gaussian dependencies is therefore a key issue in the analysis of multivariate time series. In this paper we use copulae functions with adaptively estimated time varying parameters for modelling the distribution of returns, free from the usual normality assumptions. Further, we apply copulae to estimation of Value-at-Risk (VaR) of a portfolio and show its better performance over the RiskMetrics approach, a widely used methodology for VaR estimation.

Suggested Citation

  • Giacomini, Enzo & Härdle, Wolfgang Karl & Ignatieva, Ekaterina & Spokoiny, Vladimir, 2006. "Inhomogeneous dependency modelling with time varying copulae," SFB 649 Discussion Papers 2006-075, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2006-075
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    References listed on IDEAS

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    1. Chen, Xiaohong & Fan, Yanqin & Tsyrennikov, Viktor, 2006. "Efficient Estimation of Semiparametric Multivariate Copula Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1228-1240, September.
    2. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
    3. repec:hum:wpaper:sfb649dp2005-004 is not listed on IDEAS
    4. Giacomini, Enzo & Härdle, Wolfgang Karl, 2005. "Value-at-risk calculations with time varying copulae," SFB 649 Discussion Papers 2005-004, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    5. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 125-154.
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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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