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Inhomogeneous Dependence Modeling with Time-Varying Copulae

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  • Giacomini, Enzo
  • Härdle, Wolfgang
  • 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.

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Bibliographic Info

Article provided by American Statistical Association in its journal Journal of Business and Economic Statistics.

Volume (Year): 27 (2009)
Issue (Month): 2 ()
Pages: 224-234

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Handle: RePEc:bes:jnlbes:v:27:i:2:y:2009:p:224-234

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  1. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
  2. 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.
  3. 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.
  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. 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.
  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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Cited by:
  1. Okhrin, Ostap & Okhrin, Yarema & Schmid, Wolfgang, 2013. "On the structure and estimation of hierarchical Archimedean copulas," Journal of Econometrics, Elsevier, vol. 173(2), pages 189-204.
  2. Matthias R. Fengler & Helmut Herwartz & Christian Werner, 2012. "A Dynamic Copula Approach to Recovering the Index Implied Volatility Skew," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 10(3), pages 457-493, June.
  3. Ivan Kojadinovic & Jun Yan, . "Modeling Multivariate Distributions with Continuous Margins Using the copula R Package," Journal of Statistical Software, American Statistical Association, vol. 34(i09).
  4. Almeida, Carlos & Czado, Claudia, 2012. "Efficient Bayesian inference for stochastic time-varying copula models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1511-1527.
  5. Giammarino, Flavia & Barrieu, Pauline, 2009. "A semiparametric model for the systematic factors of portfolio credit risk premia," Journal of Empirical Finance, Elsevier, vol. 16(4), pages 655-670, September.
  6. 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.
  7. 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, vol. 18(4), pages 711-727, September.
  8. 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.
  9. 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, vol. 76(C), pages 723-736.
  10. Fengler, Matthias & Okhrin, Ostap, 2012. "Realized Copula," Economics Working Paper Series 1214, University of St. Gallen, School of Economics and Political Science.
  11. 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.
  12. 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, vol. 56(11), pages 3659-3673.
  13. 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.
  14. Ostap Okhrin, 2010. "Fitting high-dimensional Copulae to Data," SFB 649 Discussion Papers SFB649DP2010-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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