Advanced Search
MyIDEAS: Login to save this paper or follow this series

Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models

Contents:

Author Info

  • Meitz, Mika

    ()
    (Department of Economics, University of Oxford)

  • Saikkonen, Pentti

    ()
    (Dept. of Statistics, University of Helsinki)

Abstract

This paper studies a class of Markov models which consist of two components. Typically, one of the components is observable and the other is unobservable or 'hidden'. Conditions under which (a form of) geometric ergodicity of the unobservable component is inherited by the joint process formed of the two components are given. This immediately implies the existence of initial values such that the joint process is strictly stationary and beta-mixing. In addition to this, conditions for beta-mixing and existence of moments for the joint process are also provided in the case of (possibly) nonstationary initial values. All these results are applied to a general model which includes as special cases various first order generalized autoregressive conditional heteroskedasticity (GARCH) and autoregressive conditional duration (ACD) models with possibly complicated nonlinear structures. The results only require mild moment assumptions and in some cases provide necessary and sufficient conditions for geometric ergodicity.

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: http://swopec.hhs.se/hastef/papers/hastef0573.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 573.

as in new window
Length: 37 pages
Date of creation: 07 Oct 2004
Date of revision: 20 Apr 2007
Publication status: Published in Econometric Theory, 2008, pages 1291-1320.
Handle: RePEc:hhs:hastef:0573

Contact details of provider:
Postal: The Economic Research Institute, Stockholm School of Economics, P.O. Box 6501, 113 83 Stockholm, Sweden
Phone: +46-(0)8-736 90 00
Fax: +46-(0)8-31 01 57
Email:
Web page: http://www.hhs.se/
More information through EDIRC

Related research

Keywords: -;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

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. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 987-1007, July.
  2. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  3. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, Elsevier, vol. 52(1-2), pages 115-127.
  4. FERNANDES, Marcelo & GRAMMIG, Joachim, 2001. "A family of autoregressive conditional duration models," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2001036, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report, Federal Reserve Bank of Minneapolis 157, Federal Reserve Bank of Minneapolis.
  6. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, Econometric Society, vol. 66(5), pages 1127-1162, September.
  7. Zhang, Michael Yuanjie & Russell, Jeffrey R. & Tsay, Ruey S., 2001. "A nonlinear autoregressive conditional duration model with applications to financial transaction data," Journal of Econometrics, Elsevier, Elsevier, vol. 104(1), pages 179-207, August.
  8. Lu, Zudi & Jiang, Zhenyu, 2001. "L1 geometric ergodicity of a multivariate nonlinear AR model with an ARCH term," Statistics & Probability Letters, Elsevier, Elsevier, vol. 51(2), pages 121-130, January.
  9. González-Rivera Gloria, 1998. "Smooth-Transition GARCH Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, De Gruyter, vol. 3(2), pages 1-20, July.
  10. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 18(01), pages 17-39, February.
  11. Lundbergh, Stefan & Terasvirta, Timo, 2002. "Evaluating GARCH models," Journal of Econometrics, Elsevier, Elsevier, vol. 110(2), pages 417-435, October.
  12. Meitz, Mika, 2005. "A necessary and sufficient condition for the strict stationarity of a family of GARCH processes," Working Paper Series in Economics and Finance, Stockholm School of Economics 601, Stockholm School of Economics.
  13. Hentschel, Ludger, 1995. "All in the family Nesting symmetric and asymmetric GARCH models," Journal of Financial Economics, Elsevier, Elsevier, vol. 39(1), pages 71-104, September.
  14. Meitz, Mika & Teräsvirta, Timo, 2004. "Evaluating models of autoregressive conditional duration," Working Paper Series in Economics and Finance, Stockholm School of Economics 557, Stockholm School of Economics, revised 13 Dec 2004.
  15. Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, Elsevier, vol. 73(1), pages 185-215, July.
  16. Francq, Christian & Zako an, Jean-Michel, 2006. "Mixing Properties Of A General Class Of Garch(1,1) Models Without Moment Assumptions On The Observed Process," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 22(05), pages 815-834, October.
  17. Shiqing Ling & Michael McAleer, 2001. "Stationarity and the Existence of Moments of a Family of GARCH Processes," ISER Discussion Paper, Institute of Social and Economic Research, Osaka University 0535, Institute of Social and Economic Research, Osaka University.
  18. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 19(02), pages 280-310, April.
  19. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 84(1), pages 61-84, January.
  20. Basrak, Bojan & Davis, Richard A. & Mikosch, Thomas, 2002. "Regular variation of GARCH processes," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 99(1), pages 95-115, May.
  21. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 6(03), pages 318-334, September.
  22. Masry, Elias & Tjøstheim, Dag, 1995. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 11(02), pages 258-289, February.
Full references (including those not matched with items on IDEAS)

Citations

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

Cited by:
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page.

Lists

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

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:hhs:hastef:0573. 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: (Helena Lundin).

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.