Inhomogeneous Dependency Modelling with Time Varying Copulae
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.
|Date of creation:||Nov 2006|
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- 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.
- 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.
- Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
- 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.
- 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.
- Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
- 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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