2024-11-0920100167-715210.1016/j.spl.2009.12.0202-s2.0-77049096704http://dx.doi.org/10.1016/j.spl.2009.12.020https://hdl.handle.net/20.500.14288/12828This 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.StatisticsProbabilityJournal Article1879-2103276117900015Q45367