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Modeling Dynamic Volatilities and Correlations under Skewness and Fat Tails

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Author Info

  • Xin Zhang

    (VU University Amsterdam)

  • Drew Creal

    (VU University Amsterdam)

  • Siem Jan Koopman

    (VU University Amsterdam)

  • Andre Lucas

    (VU University Amsterdam)

Abstract

We propose a new model for dynamic volatilities and correlations of skewed and heavy-tailed data. Our model endows the Generalized Hyperbolic distribution with time-varying parameters driven by the score of the observation density function. The key novelty in our approach is the fact that the skewed and fat-tailed shape of the distribution directly affects the dynamic behavior of the time-varying parameters. It distinguishes our approach from familiar alternatives such as the generalized autoregressive conditional heteroskedasticity model and the dynamic conditional correlation model where distributional assumptions affect the likelihood but not the parameter dynamics. We present a modified expectation-maximization algorithm to estimate the model. Simulated and empirical evidence shows that the model outperforms its close competitors if skewness and kurtosis are relevant features of the data.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 11-078/2/DSF22.

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Date of creation: 13 May 2011
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Handle: RePEc:dgr:uvatin:20110078

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Related research

Keywords: Dynamic conditional correlations; Generalized Hyperbolic distributions; Observation driven models;

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References

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  1. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  2. Drew Creal & Siem Jan Koopman & André Lucas, 2010. "A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations," Tinbergen Institute Discussion Papers 10-032/2, Tinbergen Institute.
  3. Drew Creal & Siem Jan Koopman & André Lucas, 2008. "A General Framework for Observation Driven Time-Varying Parameter Models," Tinbergen Institute Discussion Papers 08-108/4, Tinbergen Institute.
  4. Bauwens, Luc & Laurent, Sebastien, 2005. "A New Class of Multivariate Skew Densities, With Application to Generalized Autoregressive Conditional Heteroscedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 346-354, July.
  5. Fiorentini, Gabriele & Sentana, Enrique & Calzolari, Giorgio, 2003. "Maximum Likelihood Estimation and Inference in Multivariate Conditionally Heteroscedastic Dynamic Regression Models with Student t Innovations," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 532-46, October.
  6. Enrique Sentana, 2004. "Estimation and Testing of Dynamic Models with Generalised Hyperbolic Innovations," FMG Discussion Papers dp502, Financial Markets Group.
  7. Nelson, Daniel B & Foster, Dean P, 1994. "Asymptotic Filtering Theory for Univariate ARCH Models," Econometrica, Econometric Society, vol. 62(1), pages 1-41, January.
  8. Boswijk, H.P. & Weide, R. van der, 2006. "Wake me up before you GO-GARCH," CeNDEF Working Papers 06-13, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  9. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-50, July.
  10. Asai, Manabu & McAleer, Michael, 2009. "The structure of dynamic correlations in multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 150(2), pages 182-192, June.
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Citations

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Cited by:
  1. Francisco Blasques & Siem Jan Koopman & Andre Lucas, 2012. "Stationarity and Ergodicity of Univariate Generalized Autoregressive Score Processes," Tinbergen Institute Discussion Papers 12-059/4, Tinbergen Institute.
  2. Xin Zhang & Bernd Schwaab & Andre Lucas, 2011. "Conditional Probabilities and Contagion Measures for Euro Area Sovereign Default Risk," Tinbergen Institute Discussion Papers 11-176/2/DSF29, Tinbergen Institute, revised 28 Jun 2012.
  3. Harvey, A. & Sucarrat, G., 2012. "EGARCH models with fat tails, skewness and leverage," Cambridge Working Papers in Economics 1236, Faculty of Economics, University of Cambridge.

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