Stability and the Lyapounov exponent of threshold AR-ARCH Models Academic Article uri icon


  • 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. Institute of Mathematical Statistics, 2004.

published proceedings

  • The Annals of Applied Probability

author list (cited authors)

  • Cline, D., & Pu, H.

citation count

  • 59

complete list of authors

  • Cline, Daren BH||Pu, Huay-min H

publication date

  • January 2004