IDEAS home Printed from https://ideas.repec.org/p/hal/cesptp/halshs-00270719.html
   My bibliography  Save this paper

Exact Maximum Likelihood estimation for the BL-GARCH model under elliptical distributed innovations

Author

Listed:
  • Abdou Kâ Diongue

    (UGB - Université Gaston Berger de Saint-Louis Sénégal)

  • Dominique Guegan

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Rodney C. Wolff

    (School of Mathematical Sciences [Brisbane] - QUT - Queensland University of Technology [Brisbane])

Abstract

In this paper, we discuss the class of Bilinear GATRCH (BL-GARCH) models which are capable of capturing simultaneously two key properties of non-linear time series: volatility clustering and leverage effects. It has been observed often that the marginal distributions of such time series have heavy tails; thus we examine the BL-GARCH model in a general setting under some non-Normal distributions. We investigate some probabilistic properties of this model and we propose and implement a maximum likelihood estimation (MLE) methodology. To evaluate the small-sample performance of this method for the various models, a Monte Carlo study is conducted. Finally, within-sample estimation properties are studied using S&P 500 daily returns, when the features of interest manifest as volatility clustering and leverage effects.

Suggested Citation

  • Abdou Kâ Diongue & Dominique Guegan & Rodney C. Wolff, 2008. "Exact Maximum Likelihood estimation for the BL-GARCH model under elliptical distributed innovations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00270719, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00270719
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00270719
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-00270719/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Andrew J. Patton, 2004. "On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 130-168.
    2. Baillie, Richard T. & DeGennaro, Ramon P., 1990. "Stock Returns and Volatility," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(2), pages 203-214, June.
    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. Giuseppe Storti & Cosimo Vitale, 2003. "BL-GARCH models and asymmetries in volatility," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 12(1), pages 19-39, February.
    5. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
    6. McAleer, Michael, 2005. "Automated Inference And Learning In Modeling Financial Volatility," Econometric Theory, Cambridge University Press, vol. 21(1), pages 232-261, February.
    7. He, Changli & Terasvirta, Timo, 1999. "Properties of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 92(1), pages 173-192, September.
    8. Ling, Shiqing & McAleer, Michael, 2002. "Stationarity and the existence of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 109-117, January.
    9. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    10. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    11. M. C. Jones & M. J. Faddy, 2003. "A skew extension of the t‐distribution, with applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 159-174, February.
    12. Giuseppe Storti & Cosimo Vitale, 2003. "Likelihood inference in BL-GARCH models," Computational Statistics, Springer, vol. 18(3), pages 387-400, September.
    13. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    14. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    15. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
    16. Richard T. Baillie & Tim Bollerslev, 1991. "Intra-Day and Inter-Market Volatility in Foreign Exchange Rates," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(3), pages 565-585.
    17. N. H. Bingham & Rudiger Kiesel, 2002. "Semi-parametric modelling in finance: theoretical foundations," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 241-250.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Dominique Guegan & Jing Zhang, 2009. "Pricing bivariate option under GARCH-GH model with dynamic copula: application for Chinese market," PSE-Ecole d'économie de Paris (Postprint) halshs-00368336, HAL.
    2. Motelle, Sephooko & Biekpe, Nicholas, 2015. "Financial integration and stability in the Southern African development community," Journal of Economics and Business, Elsevier, vol. 79(C), pages 100-117.
    3. Charalampos Basdekis & Apostolos Christopoulos & Alexandros Gkolfinopoulos & Ioannis Katsampoxakis, 2022. "VaR as a risk management framework for the spot and futures tanker markets," Operational Research, Springer, vol. 22(4), pages 4287-4352, September.
    4. Dominique Guegan & Jing Zhang, 2009. "Pricing bivariate option under GARCH-GH model with dynamic copula: application for Chinese market," Post-Print halshs-00368336, HAL.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Abdou Kâ Diongue & Dominique Guegan & Rodney C. Wolff, 2010. "BL-GARCH model with elliptical distributed innovations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00368340, HAL.
    2. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
    3. McAleer, Michael & Chan, Felix & Marinova, Dora, 2007. "An econometric analysis of asymmetric volatility: Theory and application to patents," Journal of Econometrics, Elsevier, vol. 139(2), pages 259-284, August.
    4. Li, Ming-Yuan Leon, 2008. "Clarifying the dynamics of the relationship between option and stock markets using the threshold vector error correction model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 511-520.
    5. Amélie Charles & Olivier Darné, 2019. "The accuracy of asymmetric GARCH model estimation," International Economics, CEPII research center, issue 157, pages 179-202.
    6. Amélie Charles & Olivier Darné, 2019. "The accuracy of asymmetric GARCH model estimation," Post-Print hal-01943883, HAL.
    7. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
    8. repec:hal:wpaper:hal-01943883 is not listed on IDEAS
    9. Michael McAleer, 2009. "The Ten Commandments For Optimizing Value‐At‐Risk And Daily Capital Charges," Journal of Economic Surveys, Wiley Blackwell, vol. 23(5), pages 831-849, December.
    10. Laura Garcia‐Jorcano & Alfonso Novales, 2021. "Volatility specifications versus probability distributions in VaR forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(2), pages 189-212, March.
    11. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107034723.
    12. Deniz Erdemlioglu & Sébastien Laurent & Christopher J. Neely, 2013. "Econometric modeling of exchange rate volatility and jumps," Chapters, in: Adrian R. Bell & Chris Brooks & Marcel Prokopczuk (ed.), Handbook of Research Methods and Applications in Empirical Finance, chapter 16, pages 373-427, Edward Elgar Publishing.
    13. Neil Kellard & Denise Osborn & Jerry Coakley & John C. Nankervis & Periklis Kougoulis & Jerry Coakley, 2015. "Generalized Variance-Ratio Tests in the Presence of Statistical Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(5), pages 687-705, September.
    14. Koliai, Lyes, 2016. "Extreme risk modeling: An EVT–pair-copulas approach for financial stress tests," Journal of Banking & Finance, Elsevier, vol. 70(C), pages 1-22.
    15. Zhu, Ke & Li, Wai Keung, 2013. "A new Pearson-type QMLE for conditionally heteroskedastic models," MPRA Paper 52344, University Library of Munich, Germany.
    16. McAleer, Michael & Medeiros, Marcelo C., 2008. "A multiple regime smooth transition Heterogeneous Autoregressive model for long memory and asymmetries," Journal of Econometrics, Elsevier, vol. 147(1), pages 104-119, November.
    17. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    18. Abdou Kâ Diongue & Dominique Guegan, 2008. "Estimation of k-factor GIGARCH process : a Monte Carlo study," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00235179, HAL.
    19. Harvey, A. & Chakravarty, T., 2008. "Beta-t-(E)GARCH," Cambridge Working Papers in Economics 0840, Faculty of Economics, University of Cambridge.
    20. Wang, Yudong & Liu, Li & Ma, Feng & Wu, Chongfeng, 2016. "What the investors need to know about forecasting oil futures return volatility," Energy Economics, Elsevier, vol. 57(C), pages 128-139.
    21. Allen, David & Lizieri, Colin & Satchell, Stephen, 2020. "A comparison of non-Gaussian VaR estimation and portfolio construction techniques," Journal of Empirical Finance, Elsevier, vol. 58(C), pages 356-368.

    Corrections

    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:hal:cesptp:halshs-00270719. See general information about how to correct material in RePEc.

    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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.