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A component GARCH model with time varying weights

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  • BAUWENS, Luc

    (Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE))

  • STORTI, Giuseppe

Abstract

We present a novel GARCH model that accounts for time varying, state dependent, persistence in the volatility dynamics. The proposed model generalizes the component GARCH model of Ding and Granger (1996). The volatility is modelled as a convex combination of unobserved GARCH components where the combination weights are time varying as a function of appropriately chosen state variables. In order to make inference on the model parameters, we develop a Gibbs sampling algorithm. Adopting a fully Bayesian approach allows to easily obtain medium and long term predictions of relevant risk measures such as value at risk and expected shortfall. Finally we discuss the results of an application to a series of daily returns on the S&P500.

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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2007019.

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Date of creation: 01 Mar 2007
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Handle: RePEc:cor:louvco:2007019

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Keywords: GARCH; persistence; volatility components; value-at-risk; expected shortfall;

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References

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  1. Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July.
  2. Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(4), pages 493-530.
  3. Bauwens, L. & Lubrano, M., 1996. "Bayesian Inference on GARCH Models Using the Gibbs Sampler," G.R.E.Q.A.M. 96a21, Universite Aix-Marseille III.
  4. Baillie, Richard T. & Bollerslev, Tim, 1992. "Prediction in dynamic models with time-dependent conditional variances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 91-113.
  5. Maheu John, 2005. "Can GARCH Models Capture Long-Range Dependence?," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(4), pages 1-43, December.
  6. Luc Bauwens & Sébastien Laurent, 2002. "A New Class of Multivariate skew Densities, with Application to GARCH Models," Computing in Economics and Finance 2002 5, Society for Computational Economics.
  7. Thomas Mikosch & Catalin Starica, 2004. "Non-stationarities in financial time series, the long range dependence and the IGARCH effects," Econometrics 0412005, EconWPA.
  8. GIOT, Pierre & LAURENT, Sébastien, . "Value-at-Risk for long and short trading positions," CORE Discussion Papers RP -1707, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
  10. Lamoureux, Christopher G & Lastrapes, William D, 1990. "Persistence in Variance, Structural Change, and the GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 225-34, April.
  11. Pierre Giot and S»bastien Laurent, 2001. "Value-At-Risk For Long And Short Trading Positions," Computing in Economics and Finance 2001 94, Society for Computational Economics.
  12. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-74, October.
  13. LUBRANO, Michel, 1998. "Smooth transition GARCH models: a Bayesian perspective," CORE Discussion Papers 1998066, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  14. Pascual, Lorenzo & Romo, Juan & Ruiz, Esther, 2006. "Bootstrap prediction for returns and volatilities in GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2293-2312, May.
  15. Carlo Acerbi & Dirk Tasche, 2001. "On the coherence of Expected Shortfall," Papers cond-mat/0104295, arXiv.org, revised May 2002.
  16. Luc Bauwens & Arie Preminger & Jeroen V.K. Rombouts, 2006. "Regime switching GARCH models," Cahiers de recherche 06-08, HEC Montréal, Institut d'économie appliquée.
  17. Nelson, Daniel B., 1992. "Filtering and forecasting with misspecified ARCH models I : Getting the right variance with the wrong model," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 61-90.
  18. Lamoureux, Christopher G & Lastrapes, William D, 1993. "Forecasting Stock-Return Variance: Toward an Understanding of Stochastic Implied Volatilities," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 293-326.
  19. Gray, Stephen F., 1996. "Modeling the conditional distribution of interest rates as a regime-switching process," Journal of Financial Economics, Elsevier, vol. 42(1), pages 27-62, September.
  20. Peter Christoffersen & Sílvia Gonçalves, 2004. "Estimation Risk in Financial Risk Management," CIRANO Working Papers 2004s-15, CIRANO.
  21. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
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Citations

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Cited by:
  1. Hossein Asgharian & Charlotte Christiansen & Ai Jun Hou, 2014. "Macro-Finance Determinants of the Long-Run Stock-Bond Correlation: The DCC-MIDAS Specification," CREATES Research Papers 2014-13, School of Economics and Management, University of Aarhus.
  2. bauwens, Luc & hafner, Christian & pierret, Diane, 2011. "Multivariate volatility modeling of electricity futures," CORE Discussion Papers 2011011, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Haas, Markus & Mittnik, Stefan & Paolella, Marc S., 2009. "Asymmetric multivariate normal mixture GARCH," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2129-2154, April.
  4. Stefano Grassi & Paolo Santucci de Magistris, 2013. "It’s all about volatility (of volatility): evidence from a two-factor stochastic volatility model," CREATES Research Papers 2013-03, School of Economics and Management, University of Aarhus.
  5. Bouoiyour, Jamal & Selmi, Refk, 2013. "The controversial link between exchange rate volatility and exports: Evidence from Tunisian case," MPRA Paper 49133, University Library of Munich, Germany, revised Mar 2013.
  6. Jamal Bouoiyour & Refk Selmi, 2014. "Commodity price uncertainty and manufactured exports in Morocco and Tunisia: Some insights from a novel GARCH model," Economics Bulletin, AccessEcon, vol. 34(1), pages 220-233.
  7. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," CORE Discussion Papers 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. Bouoiyour, Jamal & Selmi, Refk, 2013. "Nonlinearities and the nexus between inflation and inflation uncertainty in Egypt: New evidence from wavelets transform framework," MPRA Paper 52414, University Library of Munich, Germany.
  9. Boudt, Kris & Daníelsson, Jón & Laurent, Sébastien, 2013. "Robust forecasting of dynamic conditional correlation GARCH models," International Journal of Forecasting, Elsevier, vol. 29(2), pages 244-257.

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