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Inhomogeneous Dependency Modelling with Time Varying Copulae

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  • Enzo Giacomini
  • Wolfgang Härdle
  • Ekaterina Ignatieva
  • Vladimir Spokoiny

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.

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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2006-075.

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Length: 51 pages
Date of creation: Nov 2006
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Handle: RePEc:hum:wpaper:sfb649dp2006-075

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Keywords: Value-at-Risk; time varying copula; adaptive estimation; nonparametric estimation.;

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References

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  1. Enzo Giacomini & Wolfgang Härdle, 2005. "Value-at-Risk Calculations with Time Varying Copulae," SFB 649 Discussion Papers SFB649DP2005-004, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, Elsevier, vol. 130(2), pages 307-335, February.
  3. Clive W. J. Granger, 2003. "Time Series Concepts for Conditional Distributions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(s1), pages 689-701, December.
  4. Xiaohong Chen & Yanqin Fan & Victor Tsyrennifov, 2004. "Efficient Estimation of Semiparametric Multivariate Copula Models," Vanderbilt University Department of Economics Working Papers 0420, Vanderbilt University Department of Economics.
  5. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification," Journal of Econometrics, Elsevier, Elsevier, vol. 135(1-2), pages 125-154.
  6. Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
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Citations

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Cited by:
  1. Giammarino, Flavia & Barrieu, Pauline, 2009. "A semiparametric model for the systematic factors of portfolio credit risk premia," Journal of Empirical Finance, Elsevier, Elsevier, vol. 16(4), pages 655-670, September.
  2. Matthias R. Fengler & Ostap Okhrin, 2012. "Realized Copula," SFB 649 Discussion Papers SFB649DP2012-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  3. Matthias Fengler & Helmut Herwartz & Christian Werner, 2010. "A dynamic copula approach to recovering the index implied volatility skew," University of St. Gallen Department of Economics working paper series 2010, Department of Economics, University of St. Gallen 1132, Department of Economics, University of St. Gallen, revised Nov 2011.
  4. Nikoloulopoulos, Aristidis K. & Joe, Harry & Li, Haijun, 2012. "Vine copulas with asymmetric tail dependence and applications to financial return data," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 56(11), pages 3659-3673.
  5. Bücher, Axel & Ruppert, Martin, 2013. "Consistent testing for a constant copula under strong mixing based on the tapered block multiplier technique," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 208-229.
  6. Syed Abul, Basher & Salem, Nechi & Hui, Zhu, 2014. "Dependence patterns across Gulf Arab stock markets: a copula approach," MPRA Paper 56566, University Library of Munich, Germany.
  7. Wied, Dominik & Dehling, Herold & van Kampen, Maarten & Vogel, Daniel, 2014. "A fluctuation test for constant Spearman’s rho with nuisance-free limit distribution," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 76(C), pages 723-736.
  8. Marc Gronwald & Janina Ketterer & Stefan Trück, 2011. "The Dependence Structure between Carbon Emission Allowances and Financial Markets - A Copula Analysis," CESifo Working Paper Series 3418, CESifo Group Munich.
  9. Boubaker, Heni & Sghaier, Nadia, 2013. "Portfolio optimization in the presence of dependent financial returns with long memory: A copula based approach," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 361-377.
  10. Okhrin, Ostap & Okhrin, Yarema & Schmid, Wolfgang, 2013. "On the structure and estimation of hierarchical Archimedean copulas," Journal of Econometrics, Elsevier, Elsevier, vol. 173(2), pages 189-204.
  11. Almeida, Carlos & Czado, Claudia, 2012. "Efficient Bayesian inference for stochastic time-varying copula models," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 56(6), pages 1511-1527.
  12. Wu, Chih-Chiang & Liang, Shin-Shun, 2011. "The economic value of range-based covariance between stock and bond returns with dynamic copulas," Journal of Empirical Finance, Elsevier, Elsevier, vol. 18(4), pages 711-727, September.
  13. Ostap Okhrin, 2010. "Fitting high-dimensional Copulae to Data," SFB 649 Discussion Papers SFB649DP2010-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  14. Ivan Kojadinovic & Jun Yan, . "Modeling Multivariate Distributions with Continuous Margins Using the copula R Package," Journal of Statistical Software, American Statistical Association, American Statistical Association, vol. 34(i09).

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