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

Author

Listed:
  • Drew Creal

    (University of Chicago, Booth School of Business)

  • Siem Jan Koopman

    (VU University Amsterdam)

  • André 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.

Suggested Citation

  • 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.
  • Handle: RePEc:tin:wpaper:20100032
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    References listed on IDEAS

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    1. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    2. 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, September.
    3. 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.
    4. Engle, Robert F. & Gallo, Giampiero M., 2006. "A multiple indicators model for volatility using intra-daily data," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 3-27.
    5. Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469.
    6. 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.
    7. Gourieroux, C. & Jasiak, J. & Sufana, R., 2009. "The Wishart Autoregressive process of multivariate stochastic volatility," Journal of Econometrics, Elsevier, vol. 150(2), pages 167-181, June.
    8. 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 339-350, July.
    9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    10. 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.
    11. Nelson, Daniel B & Foster, Dean P, 1994. "Asymptotic Filtering Theory for Univariate ARCH Models," Econometrica, Econometric Society, vol. 62(1), pages 1-41, January.
    12. 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 542-547, August.
    13. repec:cup:cbooks:9780521822893 is not listed on IDEAS
    14. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
    15. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    More about this item

    Keywords

    dynamic dependence; multivariate Student's t distribution; copula;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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