Stability and the Lyapounov exponent of threshold AR-ARCH Models
Abstract
The Lyapounov exponent and sharp conditions for geometric ergodicity are determined of a time series model with both a threshold autoregression term and threshold autoregressive conditional heteroscedastic (ARCH) errors. The conditions require studying or simulating the behavior of a bounded, ergodic Markov chain. The method of proof is based on a new approach, called the piggyback method, that exploits the relationship between the time series and the bounded chain. The piggyback method also provides a means for evaluating the Lyapounov exponent by simulation and provides a new perspective on moments, illuminating recent results for the distribution tails of GARCH models.
Keywords
Cite
@article{arxiv.math/0503547,
title = {Stability and the Lyapounov exponent of threshold AR-ARCH Models},
author = {Daren B. H. Cline and Huay-min H. Pu},
journal= {arXiv preprint arXiv:math/0503547},
year = {2016}
}
Comments
Published at http://dx.doi.org/10.1214/105051604000000431 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)