Testing for the buffered autoregressive processes

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

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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
Volume24
DOIs
Publication statusPublished - Apr 2014

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

Citation

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

Keywords

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