Stability and the Lyapounov exponent of threshold AR-ARCH Models

Daren B. H. Cline; Huay-min H. Pu

doi:10.1214/105051604000000431

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Stability and the Lyapounov exponent of threshold AR-ARCH Models

Daren B. H. Cline·Huay-min H. Pu

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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.

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BibTeX RIS

Daren B. H. Cline, Huay-min H. Pu. 2005-03-24. Stability and the Lyapounov exponent of threshold AR-ARCH Models. https://doi.org/10.1214/105051604000000431

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