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

作者：Meitz Mika^*; Saikkonen Pentti

来源：Statistics & Probability Letters, 2010, 80(7-8): 631-638.

DOI：10.1016/j.spl.2009.12.020

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 [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.

• 出版日期2010-4-1