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.
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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.
Publié le : 2004-11-14
Classification:
ARCH,
ergodicity,
Lyapounov exponent,
Markov chain,
nonlinear time series,
60G10,
60J05,
62M10,
91B84
@article{1099674083,
author = {Cline, Daren B. H. and Pu, Huay-min H.},
title = {Stability and the Lyapounov exponent of threshold AR-ARCH Models},
journal = {Ann. Appl. Probab.},
volume = {14},
number = {1},
year = {2004},
pages = { 1920-1949},
language = {en},
url = {http://dml.mathdoc.fr/item/1099674083}
}
Cline, Daren B. H.; Pu, Huay-min H. Stability and the Lyapounov exponent of threshold AR-ARCH Models. Ann. Appl. Probab., Tome 14 (2004) no. 1, pp. 1920-1949. http://gdmltest.u-ga.fr/item/1099674083/