IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1705.00535.html
   My bibliography  Save this paper

A note on the Nelson Cao inequality constraints in the GJR-GARCH model: Is there a leverage effect?

Author

Listed:
  • Stavros Stavroyiannis

Abstract

The majority of stylized facts of financial time series and several Value-at-Risk measures are modeled via univariate or multivariate GARCH processes. It is not rare that advanced GARCH models fail to converge for computational reasons, and a usual parsimonious approach is the GJR-GARCH model. There is a disagreement in the literature and the specialized econometric software, on which constraints should be used for the parameters, introducing indirectly the distinction between asymmetry and leverage. We show that the approach used by various software packages is not consistent with the Nelson-Cao inequality constraints. Implementing Monte Carlo simulations, despite of the results being empirically correct, the estimated parameters are not theoretically coherent with the Nelson-Cao constraints for ensuring positivity of conditional variances. On the other hand ruling out the leverage hypothesis, the asymmetry term in the GJR model can take negative values when typical constraints like the condition for the existence of the second and fourth moments, are imposed.

Suggested Citation

  • Stavros Stavroyiannis, 2017. "A note on the Nelson Cao inequality constraints in the GJR-GARCH model: Is there a leverage effect?," Papers 1705.00535, arXiv.org.
    • Handle: RePEc:arx:papers:1705.00535
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1705.00535
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dirk G. Baur & Brian M. Lucey, 2010. "Is Gold a Hedge or a Safe Haven? An Analysis of Stocks, Bonds and Gold," The Financial Review, Eastern Finance Association, vol. 45(2), pages 217-229, May.
    2. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    3. Michael McAleer, 2014. "Asymmetry and Leverage in Conditional Volatility Models," Econometrics, MDPI, vol. 2(3), pages 1-6, September.
    4. Nelson, Daniel B & Cao, Charles Q, 1992. "Inequality Constraints in the Univariate GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 229-235, April.
    5. 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.
    6. 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.
    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. Ling, Shiqing & McAleer, Michael, 2002. "NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS," Econometric Theory, Cambridge University Press, vol. 18(3), pages 722-729, June.
    9. Baur, Dirk G. & McDermott, Thomas K., 2010. "Is gold a safe haven? International evidence," Journal of Banking & Finance, Elsevier, vol. 34(8), pages 1886-1898, August.
    10. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    11. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    12. Davidson, James, 2004. "Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 16-29, January.
    13. Massimiliano Caporin & Michael McAleer, 2010. "Model Selection and Testing of Conditional and Stochastic Volatility Models," KIER Working Papers 724, Kyoto University, Institute of Economic Research.
    14. 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.
    15. Stavroyiannis, S. & Makris, I. & Nikolaidis, V. & Zarangas, L., 2012. "Econometric modeling and value-at-risk using the Pearson type-IV distribution," International Review of Financial Analysis, Elsevier, vol. 22(C), pages 10-17.
    16. Stavros Stavroyiannis & Leonidas Zarangas, 2013. "Out of Sample Value-at-Risk and Backtesting with the Standardized Pearson Type-IV Skewed Distribution," Panoeconomicus, Savez ekonomista Vojvodine, Novi Sad, Serbia, vol. 60(2), pages 231-247, April.
    17. Y. K. Tse, 1998. "The conditional heteroscedasticity of the yen-dollar exchange rate," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(1), pages 49-55.
    Full references (including those not matched with items on IDEAS)

    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. Degiannakis, Stavros & Xekalaki, Evdokia, 2004. "Autoregressive Conditional Heteroskedasticity (ARCH) Models: A Review," MPRA Paper 80487, University Library of Munich, Germany.
    2. Amélie Charles & Olivier Darné, 2019. "The accuracy of asymmetric GARCH model estimation," Post-Print hal-01943883, HAL.
    3. repec:hal:wpaper:hal-01943883 is not listed on IDEAS
    4. Stavroyiannis, S. & Makris, I. & Nikolaidis, V. & Zarangas, L., 2012. "Econometric modeling and value-at-risk using the Pearson type-IV distribution," International Review of Financial Analysis, Elsevier, vol. 22(C), pages 10-17.
    5. Amélie Charles & Olivier Darné, 2019. "The accuracy of asymmetric GARCH model estimation," International Economics, CEPII research center, issue 157, pages 179-202.
    6. Stavros Stavroyiannis & Leonidas Zarangas, 2013. "Out of Sample Value-at-Risk and Backtesting with the Standardized Pearson Type-IV Skewed Distribution," Panoeconomicus, Savez ekonomista Vojvodine, Novi Sad, Serbia, vol. 60(2), pages 231-247, April.
    7. Angelidis, Timotheos & Degiannakis, Stavros, 2007. "Backtesting VaR Models: A Τwo-Stage Procedure," MPRA Paper 96327, University Library of Munich, Germany.
    8. CHIA-LIN CHANG & MICHAEL McALEER & ROENGCHAI TANSUCHAT, 2012. "Modelling Long Memory Volatility In Agricultural Commodity Futures Returns," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(02), pages 1-27.
    9. Mehmet Sahiner, 2022. "Forecasting volatility in Asian financial markets: evidence from recursive and rolling window methods," SN Business & Economics, Springer, vol. 2(10), pages 1-74, October.
    10. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    11. Carl Lönnbark, 2016. "Asymmetry with respect to the memory in stock market volatilities," Empirical Economics, Springer, vol. 50(4), pages 1409-1419, June.
    12. Adnen Ben Nasr & Ahdi Noomen Ajmi & Rangan Gupta, 2014. "Modelling the volatility of the Dow Jones Islamic Market World Index using a fractionally integrated time-varying GARCH (FITVGARCH) model," Applied Financial Economics, Taylor & Francis Journals, vol. 24(14), pages 993-1004, July.
    13. Timotheos Angelidis & Stavros Degiannakis, 2007. "Backtesting VaR Models: An Expected Shortfall Approach," Working Papers 0701, University of Crete, Department of Economics.
    14. Dark Jonathan Graeme, 2010. "Estimation of Time Varying Skewness and Kurtosis with an Application to Value at Risk," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(2), pages 1-50, March.
    15. 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.
    16. Zouheir Mighri, 2018. "On the Dynamic Linkages Among International Emerging Currencies," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 16(2), pages 427-473, June.
    17. Saker Sabkha & Christian de Peretti, 2018. "On the performances of Dynamic Conditional Correlation models in the Sovereign CDS market and the corresponding bond market," Working Papers hal-01710398, HAL.
    18. Yanlin Shi & Yang Yang, 2018. "Modeling High Frequency Data with Long Memory and Structural Change: A-HYEGARCH Model," Risks, MDPI, vol. 6(2), pages 1-28, March.
    19. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    20. Saker Sabkha & Christian de Peretti, 2022. "On the performances of Dynamic Conditional Correlation models in the Sovereign CDS market and the corresponding bond market," Post-Print hal-01710398, HAL.
    21. Olusanya E. Olubusoye & OlaOluwa S. Yaya, 2016. "Time series analysis of volatility in the petroleum pricing markets: the persistence, asymmetry and jumps in the returns series," OPEC Energy Review, Organization of the Petroleum Exporting Countries, vol. 40(3), pages 235-262, September.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:1705.00535. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.