Geometric Ergodicity of a Class of Markov Chains with Applications to Time Series Models

40 Pages Posted: 3 Nov 2005

See all articles by Dennis Kristensen

Dennis Kristensen

University College London; Aarhus University - CREATES; Cemmap (Centre for Microdata Methods and Practice)

Date Written: October 19, 2005

Abstract

We set up general conditions for a general non-linear Markov model to be geometrically ergodic (which implies beta-mixing of the stationary solution) and existence of certain moments. The conditions are fairly general and can be applied to most known time series models. We demonstrate the usefulness of our general result by applying it to various popular time series models. For each model, we give conditions for beta-mixing and existence of certain moments. In many cases, our conditions are weaker than those found elsewhere in the literature. In particular, we derive sufficient conditions for a class of univariate GARCH models to be geometrically ergodic without having a 2nd moment. In certain cases, the conditions are also sufficient. We also consider multivariate GARCH models and give conditions for stationarity with finite 2nd moment.

Keywords: Markov chain, geometric ergodicity, mixing, moments, GARCH, bilinear model

JEL Classification: C22, C32

Suggested Citation

Kristensen, Dennis and Kristensen, Dennis, Geometric Ergodicity of a Class of Markov Chains with Applications to Time Series Models (October 19, 2005). Available at SSRN: https://ssrn.com/abstract=831068 or http://dx.doi.org/10.2139/ssrn.831068

Dennis Kristensen (Contact Author)

University College London ( email )

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