Stability and the Lyapounov exponent of threshold AR-ARCH models

• 成果类型: Article
• 署名作者: Cline, DBH; Pu, HMH
• 署名单位: Texas A&M University System; Texas A&M University College Station
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000000431
• 发表日期: 2004
• 页码: 1920-1949
• 关键词: nonlinear time-series; geometric ergodicity; RANDOM MATRICES; autoregressive process; difference-equations; garch processes; PRODUCTS; stationarity; volatility; inference

摘要

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 abounded, 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.