Testing for the buffered autoregressive processes

Ke ZHU, Philip L. H. YU, Wai Keung LI

Research output: Contribution to journalArticle

8 Citations (Scopus)


This paper investigates a quasi-likelihood ratio (LR) test for the thresholds in buffered autoregressive processes. Under the null hypothesis of no threshold, the LR test statistic converges to a function of a centered Gaussian process. Under local alternatives, this LR test has nontrivial asymptotic power. A bootstrap method is proposed to obtain the critical value for the LR test. Simulation studies and an example are given to assess the performance of the test. The proof here is not standard and can be used in other non-linear time series models. Copyright © 2014 Institute of Statistical Science.
Original languageEnglish
Pages (from-to)971-984
JournalStatistica Sinica
Publication statusPublished - Apr 2014


Autoregressive Process
Likelihood Ratio Test
Nonlinear Time Series Model
Likelihood Ratio Test Statistic
Asymptotic Power
Local Alternatives
Bootstrap Method
Gaussian Process
Null hypothesis
Critical value
Simulation Study
Likelihood ratio test
Autoregressive process


Zhu, K., Yu, P. L. H., & Li, W. K. (2014). Testing for the buffered autoregressive processes. Statistica Sinica, 24, 971-984. doi: 10.5705/ss.2012.311


  • AR(p) model
  • Bootstrap method
  • Buffered AR(p) model
  • Likelihood ratio test
  • Marked empirical process
  • Threshold AR(p) model