Publication: A note on the geometric ergodicity of a nonlinear AR-ARCH model
Program
KU-Authors
KU Authors
Co-Authors
Saikkonen, Pentti
Advisor
Publication Date
Language
English
Type
Journal Title
Journal ISSN
Volume Title
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 [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.
Source:
Statistics and Probability Letters
Publisher:
Elsevier Science Bv
Keywords:
Subject
Statistics, Probability