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A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations

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Author Info

  • Drew Creal

    (University of Chicago, Booth School of Business)

  • Siem Jan Koopman

    (VU University Amsterdam)

  • Andr� Lucas

    (VU University Amsterdam)

Abstract

This discussion paper led to a publication in 'Journal of Business & Economic Statistics' , 29(4), 552-63. We propose a new class of observation-driven time-varying parameter models for dynamic volatilities and correlations to handle time series from heavy-tailed distributions. The model adopts generalized autoregressive score dynamics to obtain a time-varying covariance matrix of the multivariate Student's t distribution. The key novelty of our proposed model concerns the weighting of lagged squared innovations for the estimation of future correlations and volatilities. When we account for heavy tails of distributions, we obtain estimates that are more robust to large innovations. The model also admits a representation as a time-varying heavy-tailed copula which is particularly useful if the interest focuses on dependence structures. We provide an empirical illustration for a panel of daily global equity returns. This discussion paper led to a publication in the Journal of Business and Economic Statistics (2011, 29(4) 552-63.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 10-032/2.

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Date of creation: 16 Mar 2010
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Handle: RePEc:dgr:uvatin:20100032

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Web page: http://www.tinbergen.nl

Related research

Keywords: dynamic dependence; multivariate Student's t distribution; copula;

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References

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  1. Engle, Robert F & Sheppard, Kevin K, 2001. "Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH," University of California at San Diego, Economics Working Paper Series qt5s2218dp, Department of Economics, UC San Diego.
  2. Robert F. Engle & Giampiero M. Gallo, 2003. "A Multiple Indicators Model For Volatility Using Intra-Daily Data," Econometrics Working Papers Archive wp2003_07, Universita' degli Studi di Firenze, Dipartimento di Statistica "G. Parenti".
  3. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
  4. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
  5. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2006. "Analysis of high dimensional multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 134(2), pages 341-371, October.
  6. Jianqing Fan & Mingjin Wang & Qiwei Yao, 2008. "Modelling multivariate volatilities via conditionally uncorrelated components," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 679-702.
  7. Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469.
  8. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
  9. Joan Jasiak & R. Sufana & C. Gourieroux, 2005. "The Wishart Autoregressive Process of Multivariate Stochastic Volatility," Working Papers 2005_2, York University, Department of Economics.
  10. 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.
  11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
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Citations

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Cited by:
  1. Xin Zhang & Drew Creal & Siem Jan Koopman & Andre Lucas, 2011. "Modeling Dynamic Volatilities and Correlations under Skewness and Fat Tails," Tinbergen Institute Discussion Papers 11-078/2/DSF22, Tinbergen Institute.
  2. Andre Lucas & Bernd Schwaab & Xin Zhang, 2013. "Measuring Credit Risk in a Large Banking System: Econometric Modeling and Empirics," Tinbergen Institute Discussion Papers 13-063/IV/DSF56, Tinbergen Institute, revised 30 May 2013.
  3. Jiangyu Ji & Andre Lucas, 2012. "A New Semiparametric Volatility Model," Tinbergen Institute Discussion Papers 12-055/2/DSF35, Tinbergen Institute.
  4. Siem Jan Koopman & Andre Lucas & Marcel Scharth, 2012. "Predicting Time-Varying Parameters with Parameter-Driven and Observation-Driven Models," Tinbergen Institute Discussion Papers 12-020/4, Tinbergen Institute.
  5. Andres, P. & Harvey, A., 2012. "The Dyanamic Location/Scale Model: with applications to intra-day financial data," Cambridge Working Papers in Economics 1240, Faculty of Economics, University of Cambridge.
  6. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2011. "Financial Risk Measurement for Financial Risk Management," PIER Working Paper Archive 11-037, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  7. Jiangyu Ji & Andre Lucas, 2012. "A New Semiparametric Volatility Model," Tinbergen Institute Discussion Papers 12-055/2/DSF35, Tinbergen Institute.
  8. Tommaso, Proietti & Alessandra, Luati, 2012. "Maximum likelihood estimation of time series models: the Kalman filter and beyond," MPRA Paper 39600, University Library of Munich, Germany.
  9. Ito, Ryoko, 2013. "Modeling dynamic diurnal patterns in high frequency financial data," Cambridge Working Papers in Economics 1315, Faculty of Economics, University of Cambridge.
  10. 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.
  11. 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.
  12. Siem Jan Koopman & Andre Lucas & Marcel Scharth, 2012. "Predicting Time-Varying Parameters with Parameter-Driven and Observation-Driven Models," Tinbergen Institute Discussion Papers 12-020/4, Tinbergen Institute.
  13. 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.
  14. Harvey, A. & Luati, A., 2012. "Filtering with heavy tails," Cambridge Working Papers in Economics 1255, Faculty of Economics, University of Cambridge.
  15. Kris Boudt & Jon Danielsson & Siem Jan Koopman & Andre Lucas, 2012. "Regime switches in the volatility and correlation of financial institutions," Working Paper Research 227, National Bank of Belgium.
  16. Xin Zhang & Drew Creal & Siem Jan Koopman & Andre Lucas, 2011. "Modeling Dynamic Volatilities and Correlations under Skewness and Fat Tails," Tinbergen Institute Discussion Papers 11-078/2/DSF22, Tinbergen Institute.
  17. 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.
  18. 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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