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.
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Volume (Year): 80 (2010)
Issue (Month): 7-8 (April)
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- Mika Meitz & Pentti Saikkonen, 2008.
"Stability of nonlinear AR-GARCH models,"
Journal of Time Series Analysis,
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- 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.
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- 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, September. Full references (including those not matched with items on IDEAS)
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