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

Mika Meitz (mika.meitz@helsinki.fi) and Pentti Saikkonen

Koç University-TUSIAD Economic Research Forum Working Papers from Koc University-TUSIAD Economic Research Forum

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 [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.

Keywords: Nonlinear Autoregression; Autoregressive Conditional Heteroskedasticity; Nonlinear Time Series Models; Geometric Ergodicity; Mixing; Strict Stationarity; Existence of Moments; Markov Models (search for similar items in EconPapers)
JEL-codes: C10 C22 (search for similar items in EconPapers)
Pages: 15 pages
Date: 2010-01
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Journal Article: A note on the geometric ergodicity of a nonlinear AR-ARCH model (2010)
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