Advanced Search
MyIDEAS: Login

On The Stationarity Of Markov-Switching Garch Processes


Author Info

  • Abramson, Ari
  • Cohen, Israel
Registered author(s):


    Generalized autoregressive conditional heteroskedasticity (GARCH) models with Markov-switching regimes are often used for volatility analysis of financial time series. Such models imply less persistence in the conditional variance than the standard GARCH model and potentially provide a significant improvement in volatility forecast. Nevertheless, conditions for asymptotic wide-sense stationarity have been derived only for some degenerated models. In this paper, we introduce a comprehensive approach for stationarity analysis of Markov-switching GARCH models, which manipulates a backward recursion of the model s second-order moment. A recursive formulation of the state-dependent conditional variances is developed, and the corresponding conditions for stationarity are obtained. In particular, we derive necessary and sufficient conditions for the asymptotic wide-sense stationarity of two different variants of Markov-switching GARCH processes and obtain expressions for their asymptotic variances in the general case of m-state Markov chains and (p,q)-order GARCH processes.The authors thank Professor Rami Atar for helpful discussions. The authors thank the co-editor Bruce Hansen and the three anonymous referees for their helpful comments and suggestions and in particular the referee who proposed a generalization of the proof in Appendix B. This research was supported by the Israel Science Foundation (grant 1085 05).

    Download Info

    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:
    File Function: link to article abstract page
    Download Restriction: no

    Bibliographic Info

    Article provided by Cambridge University Press in its journal Econometric Theory.

    Volume (Year): 23 (2007)
    Issue (Month): 03 (June)
    Pages: 485-500

    as in new window
    Handle: RePEc:cup:etheor:v:23:y:2007:i:03:p:485-500_07

    Contact details of provider:
    Postal: The Edinburgh Building, Shaftesbury Road, Cambridge CB2 2RU UK
    Fax: +44 (0)1223 325150
    Web page:

    Related research



    No references listed on IDEAS
    You can help add them by filling out this form.


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as in new window

    Cited by:
    1. Luc Bauwens & Arie Preminger & Jeroen V. K. Rombouts, 2010. "Theory and inference for a Markov switching GARCH model," Econometrics Journal, Royal Economic Society, vol. 13(2), pages 218-244, 07.
    2. Monica Billio & Roberto Casarin & Anthony Osuntuyi, 2012. "Efficient Gibbs Sampling for Markov Switching GARCH Models," Working Papers 2012:35, Department of Economics, University of Venice "Ca' Foscari".
    3. Szabolcs Blazsek & Anna Downarowicz, 2008. "Regime switching models of hedge fund returns," Faculty Working Papers 12/08, School of Economics and Business Administration, University of Navarra.


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


    Access and download statistics


    When requesting a correction, please mention this item's handle: RePEc:cup:etheor:v:23:y:2007:i:03:p:485-500_07. 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: (Keith Waters).

    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.