IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

Asymptotic properties of QMLE for periodic asymmetric strong and semi-strong GARCH models

Listed author(s):
  • Bibi, Abdelouahab
  • Ghezal, Ahmed
Registered author(s):

    In this paper, we propose a natural extension of time-invariant coefficients threshold GARCH (TGARCH) processes to periodically time-varying coefficients (PTGARCH) one. So some theoretical probabilistic properties of such models are discussed, in particular, we establish firstly necessary and sufficient conditions which ensure the strict stationarity and ergodicity (in periodic sense) solution of PTGARCH. Secondary, we extend the standard results for the limit theory of the popular quasi-maximum likelihood estimator (QMLE) for estimating the unknown parameters of the model. More precisely, the strong consistency and the asymptotic normality of QMLE are studied in cases when the innovation process is an i.i.d (Strong case) and/or is not (Semi-strong case). The finite-sample properties of QMLE are illustrated by a Monte Carlo study. Our proposed model is applied to model the exchange rates of the Algerian Dinar against the U.S-dollar and the single European currency (Euro).

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL: https://mpra.ub.uni-muenchen.de/81126/1/MPRA_paper_81126.pdf
    File Function: original version
    Download Restriction: no

    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 81126.

    as
    in new window

    Length:
    Date of creation: 04 Sep 2017
    Handle: RePEc:pra:mprapa:81126
    Contact details of provider: Postal:
    Ludwigstra├če 33, D-80539 Munich, Germany

    Phone: +49-(0)89-2180-2459
    Fax: +49-(0)89-2180-992459
    Web page: https://mpra.ub.uni-muenchen.de

    More information through EDIRC

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

    as
    in new window


    1. Escanciano, Juan Carlos, 2009. "Quasi-Maximum Likelihood Estimation Of Semi-Strong Garch Models," Econometric Theory, Cambridge University Press, vol. 25(02), pages 561-570, April.
    2. Wang, Hui & Pan, Jiazhu, 2014. "Normal mixture quasi maximum likelihood estimation for non-stationary TGARCH(1,1) models," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 117-123.
    3. Pan, Jiazhu & Wang, Hui & Tong, Howell, 2008. "Estimation and tests for power-transformed and threshold GARCH models," Journal of Econometrics, Elsevier, vol. 142(1), pages 352-378, January.
    4. 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.
    5. Philip Hans Franses & Richard Paap, 2000. "Modelling day-of-the-week seasonality in the S&P 500 index," Applied Financial Economics, Taylor & Francis Journals, vol. 10(5), pages 483-488.
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. Aknouche, Abdelhakim & Guerbyenne, Hafida, 2009. "Periodic stationarity of random coefficient periodic autoregressions," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 990-996, April.
    8. Gonzalez-Rivera, Gloria & Drost, Feike C., 1999. "Efficiency comparisons of maximum-likelihood-based estimators in GARCH models," Journal of Econometrics, Elsevier, vol. 93(1), pages 93-111, November.
    9. Francq, Christian & Zakoian, Jean-Michel, 2013. "Inference in non stationary asymmetric garch models," MPRA Paper 44901, University Library of Munich, Germany.
    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. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(01), pages 29-52, March.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:81126. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter)

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.