A note on the geometric ergodicity of a nonlinear AR–ARCH model
AbstractThis 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 [Journal of Time Series Analysis, 26 (2005), 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.
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Bibliographic InfoPaper provided by Koc University-TUSIAD Economic Research Forum in its series Koç University-TUSIAD Economic Research Forum Working Papers with number 1003.
Length: 15 pages
Date of creation: Jan 2010
Date of revision:
Nonlinear Autoregression; Autoregressive Conditional Heteroskedasticity; Nonlinear Time Series Models; Geometric Ergodicity; Mixing; Strict Stationarity; Existence of Moments; Markov Models;
Other versions of this item:
- Meitz, Mika & Saikkonen, Pentti, 2010. "A note on the geometric ergodicity of a nonlinear AR-ARCH model," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 631-638, April.
- C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-01-30 (All new papers)
- NEP-ECM-2010-01-30 (Econometrics)
- NEP-ETS-2010-01-30 (Econometric Time Series)
- NEP-ORE-2010-01-30 (Operations Research)
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.:
- 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.
- 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," Working Paper Series in Economics and Finance 632, Stockholm School of Economics.
- 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).
- 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.
- 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.
- 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.
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