IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v87y2014icp121-124.html

A note on integrated periodic GARCH processes

Author

Listed:
  • Bibi, Abdelouahab
  • Lescheb, Ines

Abstract

This note examines some probabilistic properties of periodic and integrated periodic generalized autoregressive conditionally heteroskedasticitic ((I)PGARCH) processes. In these models, the parameters are allowed to switch between different regimes and thus constitute an important subclass of switching GARCH process. We show that, similarly to the classical IGARCH processes, a stationary (in periodic sense) solution with infinite variance for the IPGARCH processes may exist.

Suggested Citation

  • Bibi, Abdelouahab & Lescheb, Ines, 2014. "A note on integrated periodic GARCH processes," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 121-124.
    • Handle: RePEc:eee:stapro:v:87:y:2014:i:c:p:121-124
    DOI: 10.1016/j.spl.2014.01.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715214000182
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2014.01.007?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Bollerslev, Tim & Ghysels, Eric, 1996. "Periodic Autoregressive Conditional Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 139-151, April.
    2. I. V. Basawa & Robert Lund, 2001. "Large Sample Properties of Parameter Estimates for Periodic ARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(6), pages 651-663, November.
    3. 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.
    4. Abdelhakim Aknouche & Abdelouahab Bibi, 2009. "Quasi‐maximum likelihood estimation of periodic GARCH and periodic ARMA‐GARCH processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 19-46, January.
    5. Bibi, Abdelouahab & Lescheb, Ines, 2010. "Strong consistency and asymptotic normality of least squares estimators for PGARCH and PARMA-PGARCH models," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1532-1542, October.
    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. Aknouche, Abdelhakim & Bentarzi, Mohamed, 2025. "Efficient two-stage estimation of cyclical ARCH models," MPRA Paper 127417, University Library of Munich, Germany.
    2. repec:dau:papers:123456789/5529 is not listed on IDEAS
    3. Aknouche, Abdelhakim & Demmouche, Nacer & Touche, Nassim, 2018. "Bayesian MCMC analysis of periodic asymmetric power GARCH models," MPRA Paper 91136, University Library of Munich, Germany.
    4. Aknouche, Abdelhakim & Al-Eid, Eid & Demouche, Nacer, 2016. "Generalized quasi-maximum likelihood inference for periodic conditionally heteroskedastic models," MPRA Paper 75770, University Library of Munich, Germany, revised 19 Dec 2016.
    5. repec:dau:papers:123456789/2285 is not listed on IDEAS
    6. Aknouche, Abdelhakim & Guerbyenne, Hafida, 2009. "Periodic stationarity of random coefficient periodic autoregressions," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 990-996, April.
    7. Aknouche, Abdelhakim, 2013. "Periodic autoregressive stochastic volatility," MPRA Paper 69571, University Library of Munich, Germany, revised 2015.
    8. Regnard, Nazim & Zakoïan, Jean-Michel, 2011. "A conditionally heteroskedastic model with time-varying coefficients for daily gas spot prices," Energy Economics, Elsevier, vol. 33(6), pages 1240-1251.
    9. Daniel Dzikowski & Carsten Jentsch, 2024. "Structural Periodic Vector Autoregressions," Papers 2401.14545, arXiv.org, revised Aug 2025.
    10. Abdelhakim Aknouche & Abdelouahab Bibi, 2009. "Quasi‐maximum likelihood estimation of periodic GARCH and periodic ARMA‐GARCH processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 19-46, January.
    11. Christian Francq & Roch Roy & Abdessamad Saidi, 2011. "Asymptotic Properties of Weighted Least Squares Estimation in Weak PARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(6), pages 699-723, November.
    12. Nadia Boussaha & Faycal Hamdi & Saïd Souam, 2018. "Multivariate Periodic Stochastic Volatility Models: Applications to Algerian dinar exchange rates and oil prices modeling," EconomiX Working Papers 2018-14, University of Paris Nanterre, EconomiX.
    13. Aknouche, Abdelhakim & Almohaimeed, Bader & Dimitrakopoulos, Stefanos, 2020. "Periodic autoregressive conditional duration," MPRA Paper 101696, University Library of Munich, Germany, revised 08 Jul 2020.
    14. Y. Boubacar Maïnassara & A. Ilmi Amir, 2024. "Portmanteau tests for periodic ARMA models with dependent errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 45(2), pages 164-188, March.
    15. Dzikowski, Daniel & Jentsch, Carsten, 2025. "Structural periodic vector autoregressions," Journal of Econometrics, Elsevier, vol. 252(PA).
    16. Nazim Regnard & Jean‐Michel Zakoïan, 2010. "Structure and estimation of a class of nonstationary yet nonexplosive GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 348-364, September.
    17. Aknouche, Abdelhakim & Bentarzi, Mohamed, 2008. "On the existence of higher-order moments of periodic GARCH models," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3262-3268, December.
    18. Koopman, Siem Jan & Ooms, Marius & Carnero, M. Angeles, 2007. "Periodic Seasonal Reg-ARFIMAGARCH Models for Daily Electricity Spot Prices," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 16-27, March.
    19. Bibi, Abdelouahab & Lescheb, Ines, 2010. "Strong consistency and asymptotic normality of least squares estimators for PGARCH and PARMA-PGARCH models," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1532-1542, October.
    20. Abdelhakim Aknouche & Eid Al-Eid & Nacer Demouche, 2018. "Generalized quasi-maximum likelihood inference for periodic conditionally heteroskedastic models," Statistical Inference for Stochastic Processes, Springer, vol. 21(3), pages 485-511, October.
    21. Corbet, Shaen & Larkin, Charles & McMullan, Caroline, 2020. "The impact of industrial incidents on stock market volatility," Research in International Business and Finance, Elsevier, vol. 52(C).
    22. Felix Chan & Michael McAleer, 2003. "Estimating smooth transition autoregressive models with GARCH errors in the presence of extreme observations and outliers," Applied Financial Economics, Taylor & Francis Journals, vol. 13(8), pages 581-592.

    More about this item

    Keywords

    ;
    ;
    ;

    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:eee:stapro:v:87:y:2014:i:c:p:121-124. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.