IDEAS home Printed from
   My bibliography  Save this article

Regular Variation and Extremal Dependence of GARCH Residuals with Application to Market Risk Measures


  • Fabrizio Laurini
  • Jonathan Tawn


Stock returns exhibit heavy tails and volatility clustering. These features, motivating the use of GARCH models, make it difficult to predict times and sizes of losses that might occur. Estimation of losses, like the Value-at-Risk, often assume that returns, normalized by the level of volatility, are Gaussian. Often under ARMA-GARCH modeling, such scaled returns are heavy tailed and show extremal dependence, whose strength reduces when increasing extreme levels. We model heavy tails of scaled returns with generalized Pareto distributions, while extremal dependence can be reduced by declustering data.

Suggested Citation

  • Fabrizio Laurini & Jonathan Tawn, 2009. "Regular Variation and Extremal Dependence of GARCH Residuals with Application to Market Risk Measures," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 146-169.
  • Handle: RePEc:taf:emetrv:v:28:y:2009:i:1-3:p:146-169 DOI: 10.1080/07474930802387985

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    2. Brownlees, C.T. & Gallo, G.M., 2006. "Financial econometric analysis at ultra-high frequency: Data handling concerns," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2232-2245, December.
    3. Ghysels, Eric & Gourieroux, Christian & Jasiak, Joann, 2004. "Stochastic volatility duration models," Journal of Econometrics, Elsevier, vol. 119(2), pages 413-433, April.
    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. repec:adr:anecst:y:2000:i:60:p:05 is not listed on IDEAS
    6. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    7. Joachim Grammig & Kai-Oliver Maurer, 2000. "Non-monotonic hazard functions and the autoregressive conditional duration model," Econometrics Journal, Royal Economic Society, vol. 3(1), pages 16-38.
    8. De Luca Giovanni & Gallo Giampiero M., 2004. "Mixture Processes for Financial Intradaily Durations," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-20, May.
    9. BAUWENS, Luc & VEREDAS, David, 1999. "The stochastic conditional duration model: a latent factor model for the analysis of financial durations," CORE Discussion Papers 1999058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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. Ghysels, Eric, 2000. "Some Econometric Recipes for High-Frequency Data Cooking," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 154-163, April.
    12. Ken Nyholm, 2002. "Estimating the Probability of Informed Trading," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 25(4), pages 485-505.
    13. Giovanni De Luca & Paola Zuccolotto, 2003. "Finite and infinite mixtures for financial durations," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 431-455.
    14. Zhang, Michael Yuanjie & Russell, Jeffrey R. & Tsay, Ruey S., 2001. "A nonlinear autoregressive conditional duration model with applications to financial transaction data," Journal of Econometrics, Elsevier, vol. 104(1), pages 179-207, August.
    15. Jaffe, Jeffrey F & Winkler, Robert L, 1976. "Optimal Speculation against an Efficient Market," Journal of Finance, American Finance Association, vol. 31(1), pages 49-61, March.
    16. Ken Nyholm, 2003. "Inferring the private information content of trades: a regime-switching approach The views presented in the paper are not necessarily shared by the European Central Bank," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(4), pages 457-470.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. So, Mike K.P. & Chan, Raymond K.S., 2014. "Bayesian analysis of tail asymmetry based on a threshold extreme value model," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 568-587.
    2. Zhang, Zhengjun & Zhu, Bin, 2016. "Copula structured M4 processes with application to high-frequency financial data," Journal of Econometrics, Elsevier, vol. 194(2), pages 231-241.


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:emetrv:v:28:y:2009:i:1-3:p:146-169. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.