CONSISTENCY AND LIMITING DISTRIBUTION OF THE LEAST-SQUARES ESTIMATOR OF A THRESHOLD AUTOREGRESSIVE MODEL

• 成果类型: Article
• 署名作者: CHAN, KS
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176349040
• 发表日期: 1993
• 页码: 520-533
• 关键词: ar(1) model; ergodicity

摘要

It is shown that, under some regularity conditions, the least squares estimator of a stationary ergodic threshold autoregressive model is strongly consistent. The limiting distribution of the least squares estimator is derived. It is shown that the estimator of the threshold parameter is N consistent and its limiting distribution is related to a compound Poisson process.