Advanced Search
MyIDEAS: Login

A note on the geometric ergodicity of a nonlinear AR-ARCH model

Contents:

Author Info

  • Meitz, Mika
  • Saikkonen, Pentti

Abstract

This note studies the geometric ergodicity of nonlinear autoregressive models with conditionally heteroskedastic errors. A nonlinear autoregression of order p (AR(p)) with the conditional variance specified as the conventional linear autoregressive conditional heteroskedasticity model of order q (ARCH(q)) is considered. Conditions under which the Markov chain representation of this nonlinear AR-ARCH model is geometrically ergodic and has moments of known order are provided. The obtained results complement those of Liebscher [Liebscher, E., 2005. Towards a unified approach for proving geometric ergodicity and mixing properties of nonlinear autoregressive processes, Journal of Time Series Analysis, 26, 669-689] by showing how his approach based on the concept of the joint spectral radius of a set of matrices can be extended to establish geometric ergodicity in nonlinear autoregressions with conventional ARCH(q) errors.

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://www.sciencedirect.com/science/article/B6V1D-4Y2PGSC-7/2/47fdd9c199e3efeb4e237919f264f8f4
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Bibliographic Info

Article provided by Elsevier in its journal Statistics & Probability Letters.

Volume (Year): 80 (2010)
Issue (Month): 7-8 (April)
Pages: 631-638

as in new window
Handle: RePEc:eee:stapro:v:80:y:2010:i:7-8:p:631-638

Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description

Order Information:
Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
Web: https://shop.elsevier.com/order?id=505573&ref=505573_01_ooc_1&version=01

Related research

Keywords:

Other versions of this item:

Find related papers by JEL classification:

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. Lu, Zudi & Jiang, Zhenyu, 2001. "L1 geometric ergodicity of a multivariate nonlinear AR model with an ARCH term," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 121-130, January.
  2. Mika Meitz & Pentti Saikkonen, 2008. "Stability of nonlinear AR-GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(3), pages 453-475, 05.
  3. Cline, Daren B. H. & Pu, Huay-min H., 1998. "Verifying irreducibility and continuity of a nonlinear time series," Statistics & Probability Letters, Elsevier, vol. 40(2), pages 139-148, September.
  4. Daren B. H. Cline, 2007. "Evaluating the Lyapounov Exponent and Existence of Moments for Threshold AR-ARCH Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(2), pages 241-260, 03.
  5. 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, vol. 11(02), pages 258-289, February.
  6. Basrak, Bojan & Davis, Richard A. & Mikosch, Thomas, 2002. "Regular variation of GARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 95-115, May.
  7. Eckhard Liebscher, 2005. "Towards a Unified Approach for Proving Geometric Ergodicity and Mixing Properties of Nonlinear Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(5), pages 669-689, 09.
Full references (including those not matched with items on IDEAS)

Citations

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:eee:stapro:v:80:y:2010:i:7-8:p:631-638. 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: (Zhang, Lei).

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.