IDEAS home Printed from https://ideas.repec.org/a/spr/metron/v79y2021i3d10.1007_s40300-021-00221-w.html
   My bibliography  Save this article

M-Estimate for the stationary hyperbolic GARCH models

Author

Listed:
  • Lanciné Bamba

    (Institut National Polytechnique Félix Houphouët-Boigny)

  • Ouagnina Hili

    (Institut National Polytechnique Félix Houphouët-Boigny)

  • Abdou Kâ Diongue

    (Université Gaston Berger de Saint-Louis)

  • Assi N’Guessan

    (Université de Lille)

Abstract

In this manuscrit, we propose two classes of M-estimates for the hyperbolic GARCH models. The first class called M-estimate is defined by minimizing of a convenient bounded loss function. The second, called BM-estimate is a modified version of the first with a mechanism that limits the propagation of the effect of outliers in the conditional variance. The asymptotic properties of these classes of M-estimates are established. According to the Monte Carlo study, we compare the performance of the M and BM-estimates with that of the quasi-maximum likelihood (QML) estimate. We show that the proposed M and BM-estimates are less affected by outliers than the QML-estimate. Moreover, in the last part, an empirical example indicates that the studied M-estimate is the best for the out-of-sample forecasting.

Suggested Citation

  • Lanciné Bamba & Ouagnina Hili & Abdou Kâ Diongue & Assi N’Guessan, 2021. "M-Estimate for the stationary hyperbolic GARCH models," METRON, Springer;Sapienza Università di Roma, vol. 79(3), pages 303-351, December.
    • Handle: RePEc:spr:metron:v:79:y:2021:i:3:d:10.1007_s40300-021-00221-w
    DOI: 10.1007/s40300-021-00221-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40300-021-00221-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s40300-021-00221-w?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. GIRAITIS, Liudas & KOKOSZKA, Piotr & LEIPUS, Remigijus & TEYSSIÈRE, Gilles, 2003. "Rescaled variance and related tests for long memory in volatility and levels," LIDAM Reprints CORE 1594, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Li, Muyi & Li, Wai Keung & Li, Guodong, 2015. "A new hyperbolic GARCH model," Journal of Econometrics, Elsevier, vol. 189(2), pages 428-436.
    3. 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.
    4. Nora Muler & Victor J. Yohai, 2002. "Robust estimates for arch processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(3), pages 341-375, May.
    5. 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.
    6. Kwan, Wilson & Li, Wai Keung & Li, Guodong, 2012. "On the estimation and diagnostic checking of the ARFIMA–HYGARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3632-3644.
    7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    8. 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.
    9. 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.
    10. 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.
    11. Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus & Teyssiere, Gilles, 2003. "Rescaled variance and related tests for long memory in volatility and levels," Journal of Econometrics, Elsevier, vol. 112(2), pages 265-294, February.
    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. Charfeddine, Lanouar & Ajmi, Ahdi Noomen, 2013. "The Tunisian stock market index volatility: Long memory vs. switching regime," Emerging Markets Review, Elsevier, vol. 16(C), pages 170-182.
    2. Li, Muyi & Li, Wai Keung & Li, Guodong, 2015. "A new hyperbolic GARCH model," Journal of Econometrics, Elsevier, vol. 189(2), pages 428-436.
    3. Kwan, Wilson & Li, Wai Keung & Li, Guodong, 2012. "On the estimation and diagnostic checking of the ARFIMA–HYGARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3632-3644.
    4. Kunal Saha & Vinodh Madhavan & Chandrashekhar G. R. & David McMillan, 2020. "Pitfalls in long memory research," Cogent Economics & Finance, Taylor & Francis Journals, vol. 8(1), pages 1733280-173, January.
    5. Carl Lönnbark, 2016. "Asymmetry with respect to the memory in stock market volatilities," Empirical Economics, Springer, vol. 50(4), pages 1409-1419, June.
    6. Muyi Li & Wai Keung Li & Guodong Li, 2013. "On Mixture Memory Garch Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(6), pages 606-624, November.
    7. Ranjit Kumar Paul & Bishal Gurung & Sandipan Samanta, 2015. "Analyzing the Effect of Dual Long Memory Process in Forecasting Agricultural Prices in Different Markets of India," International Journal of Empirical Finance, Research Academy of Social Sciences, vol. 4(4), pages 235-249.
    8. Trino-Manuel Ñíguez, 2003. "Volatility And Var Forecasting For The Ibex-35 Stock-Return Index Using Figarch-Type Processes And Different Evaluation Criteria," Working Papers. Serie AD 2003-33, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    9. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2005. "Volatility forecasting," CFS Working Paper Series 2005/08, Center for Financial Studies (CFS).
    10. Pan, Qunxing & Li, Peng & Du, Xiuli, 2023. "An improved FIGARCH model with the fractional differencing operator (1-νL)d," Finance Research Letters, Elsevier, vol. 55(PB).
    11. repec:wyi:journl:002190 is not listed on IDEAS
    12. David McMillan & Raquel Quiroga Garcia, 2009. "Intra-day volatility forecasts," Applied Financial Economics, Taylor & Francis Journals, vol. 19(8), pages 611-623.
    13. Walther, Thomas & Klein, Tony & Thu, Hien Pham & Piontek, Krzysztof, 2017. "True or spurious long memory in European non-EMU currencies," Research in International Business and Finance, Elsevier, vol. 40(C), pages 217-230.
    14. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    15. 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.
    16. Bhaskar Bagchi & Biswajit Paul, 2023. "Effects of Crude Oil Price Shocks on Stock Markets and Currency Exchange Rates in the Context of Russia-Ukraine Conflict: Evidence from G7 Countries," JRFM, MDPI, vol. 16(2), pages 1-18, January.
    17. David G. McMillan & Pako Thupayagale, 2009. "The efficiency of African equity markets," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 26(4), pages 275-292, October.
    18. Aloui, Chaker & Mabrouk, Samir, 2010. "Value-at-risk estimations of energy commodities via long-memory, asymmetry and fat-tailed GARCH models," Energy Policy, Elsevier, vol. 38(5), pages 2326-2339, May.
    19. David McMillan & Alan Speight, 2006. "Heterogeneous information flows and intra-day volatility dynamics: evidence from the UK FTSE-100 stock index futures market," Applied Financial Economics, Taylor & Francis Journals, vol. 16(13), pages 959-972.
    20. Nikolaos A. Kyriazis, 2021. "A Survey on Volatility Fluctuations in the Decentralized Cryptocurrency Financial Assets," JRFM, MDPI, vol. 14(7), pages 1-46, June.
    21. Abakah, Emmanuel Joel Aikins & Gil-Alana, Luis Alberiko & Madigu, Godfrey & Romero-Rojo, Fatima, 2020. "Volatility persistence in cryptocurrency markets under structural breaks," International Review of Economics & Finance, Elsevier, vol. 69(C), pages 680-691.

    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:spr:metron:v:79:y:2021:i:3:d:10.1007_s40300-021-00221-w. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.