Stability and the Lyapounov exponent of threshold AR-ARCH Models

By D. Cline, H. H. Pu. 2004

66 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/171057bd41f681d679d6857040de1f311fe1d1ea

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Citations in the corpus

Ergodicity and invertibility of threshold moving-average models (2007, unknown): “Further related results can be found in Chen and Tsay (1991), Brockwell et al. (1992), Liu and Susko (1992), An and Huang (1996), An and Chen (1997), Liu et al. (1997), Ling (1999), Cline and Pu (1999, 2004), Lanne and Saikkonen (2005), Liebscher (2005) and others.”
Stability of nonlinear AR‐GARCH models (2008, unknown): “These results have been extended to allow for ARCH-, but not GARCH-, type conditional heteroskedasticity by Masry and Tj� stheim (1995), Cline and Pu (1998, 1999, 2004) , Lu (1998), Chen and Chen (2001), Hwang and Woo (2001), Lu and Jiang (2001), Liebscher (2005), and Saikkonen (2007).”
On the least squares estimation of multiple-regime threshold autoregressive models (2012, background): “At the same time, probabilistic structures of TARmodels were studied intensively by Chan et al. (1985), Chan and Tong (1985), Chen and Tsay (1991), Brockwell et al. (1992), Liu and Susko (1992), An andHuang (1996), Ling (1999), Cline and Pu (2004) and so on.”