A note on the geometric ergodicity of a nonlinear AR-ARCH model
This note studies the geometric ergodicity of nonlinear autoregressive models with conditionally heteroskedastic errors. A nonlinear autoregression of order pÂ (AR(p)) with the conditional variance specified as the conventional linear autoregressive conditional heteroskedasticity model of order qÂ (ARCH(q)) is considered. Conditions under which the Markov chain representation of this nonlinear AR-ARCHÂ 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.
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.
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.
Volume (Year): 80 (2010)
Issue (Month): 7-8 (April)
|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|
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.:
- MEITZ, Mika & SAIKKONEN, Pentti, 2006.
"Stability of nonlinear AR-GARCH models,"
CORE Discussion Papers
2006078, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Mika Meitz & Pentti Saikkonen, 2007. "Stability of nonlinear AR-GARCH models," Economics Series Working Papers 328, University of Oxford, Department of Economics.
- Meitz, Mika & Saikkonen, Pentti, 2006. "Stability of nonlinear AR-GARCH models," SSE/EFI Working Paper Series in Economics and Finance 632, Stockholm School of Economics.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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)
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: (Dana Niculescu)
If references are entirely missing, you can add them using this form.