Publication: A note on the geometric ergodicity of a nonlinear AR-ARCH model
Program
KU-Authors
KU Authors
Co-Authors
Saikkonen, Pentti
Publication Date
Language
Type
Embargo Status
Journal Title
Journal ISSN
Volume Title
Alternative 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
Publisher
Elsevier Science Bv
Subject
Statistics, Probability
Citation
Has Part
Source
Statistics and Probability Letters
Book Series Title
Edition
DOI
10.1016/j.spl.2009.12.020