IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v27y2006i6p923-942.html
   My bibliography  Save this article

Integer‐Valued GARCH Process

Author

Listed:
  • René Ferland
  • Alain Latour
  • Driss Oraichi

Abstract

. An integer‐valued analogue of the classical generalized autoregressive conditional heteroskedastic (GARCH) (p,q) model with Poisson deviates is proposed and a condition for the existence of such a process is given. For the case p = 1, q = 1, it is explicitly shown that an integer‐valued GARCH process is a standard autoregressive moving average (1, 1) process. The problem of maximum likelihood estimation of parameters is treated. An application of the model to a real time series with a numerical example is given.

Suggested Citation

  • René Ferland & Alain Latour & Driss Oraichi, 2006. "Integer‐Valued GARCH Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(6), pages 923-942, November.
    • Handle: RePEc:bla:jtsera:v:27:y:2006:i:6:p:923-942
    DOI: 10.1111/j.1467-9892.2006.00496.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9892.2006.00496.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9892.2006.00496.x?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
    ---><---

    References listed on IDEAS

    as
    1. Tina Hviid Rydberg & Neil Shephard, 2000. "BIN Models for Trade-by-Trade Data. Modelling the Number of Trades in a Fixed Interval of Time," Econometric Society World Congress 2000 Contributed Papers 0740, Econometric Society.
    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. Huang, Lorick & Khabou, Mahmoud, 2023. "Nonlinear Poisson autoregression and nonlinear Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 201-241.
    2. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos, 2020. "On an integer-valued stochastic intensity model for time series of counts," MPRA Paper 105406, University Library of Munich, Germany.
    3. Carallo, Giulia & Casarin, Roberto & Robert, Christian P., 2024. "Generalized Poisson difference autoregressive processes," International Journal of Forecasting, Elsevier, vol. 40(4), pages 1359-1390.
    4. Christian H. Weiß, 2017. "On Eigenvalues of the Transition Matrix of Some Count-Data Markov Chains," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 997-1007, September.
    5. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos & Touche, Nassim, 2019. "Integer-valued stochastic volatility," MPRA Paper 91962, University Library of Munich, Germany, revised 04 Feb 2019.
    6. Quoreshi, Shahiduzzaman, 2005. "Modelling High Frequency Financial Count Data," Umeå Economic Studies 656, Umeå University, Department of Economics.
    7. James McCulloch, 2007. "Relative volume as a doubly stochastic binomial point process," Quantitative Finance, Taylor & Francis Journals, vol. 7(1), pages 55-62.
    8. Anne Leucht & Michael Neumann, 2013. "Degenerate $$U$$ - and $$V$$ -statistics under ergodicity: asymptotics, bootstrap and applications in statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(2), pages 349-386, April.
    9. Abdelhakim Aknouche & Christian Francq, 2022. "Stationarity and ergodicity of Markov switching positive conditional mean models," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 436-459, May.
    10. Chiranjit Dutta & Kara Karpman & Sumanta Basu & Nalini Ravishanker, 2023. "Review of Statistical Approaches for Modeling High-Frequency Trading Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 1-48, May.
    11. Aknouche, Abdelhakim & Bentarzi, Wissam & Demouche, Nacer, 2017. "On periodic ergodicity of a general periodic mixed Poisson autoregression," MPRA Paper 79650, University Library of Munich, Germany.
    12. Aknouche, Abdelhakim & Almohaimeed, Bader & Dimitrakopoulos, Stefanos, 2020. "Forecasting transaction counts with integer-valued GARCH models," MPRA Paper 101779, University Library of Munich, Germany, revised 11 Jul 2020.

    More about this item

    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:bla:jtsera:v:27:y:2006:i:6:p:923-942. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.