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Testing for the buffered autoregressive processes

Author

Listed:
  • Zhu, Ke
  • Yu, Philip L.H.
  • Li, Wai Keung

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. Furthermore, a bootstrap method is proposed to obtain the critical value for our LR test. Simulation studies and one real example are given to assess the performance of this LR test. The proof in this paper is not standard and can be used in other non-linear time series models.

Suggested Citation

  • Zhu, Ke & Yu, Philip L.H. & Li, Wai Keung, 2013. "Testing for the buffered autoregressive processes," MPRA Paper 51706, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:51706
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    File URL: https://mpra.ub.uni-muenchen.de/51706/1/MPRA_paper_51706.pdf
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    References listed on IDEAS

    as
    1. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    2. Potter, Simon M, 1995. "A Nonlinear Approach to US GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(2), pages 109-125, April-Jun.
    3. Hansen, Bruce E., 1999. "Threshold effects in non-dynamic panels: Estimation, testing, and inference," Journal of Econometrics, Elsevier, vol. 93(2), pages 345-368, December.
    4. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
    5. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    6. Pham, Tuan D. & Tran, Lanh T., 1985. "Some mixing properties of time series models," Stochastic Processes and their Applications, Elsevier, vol. 19(2), pages 297-303, April.
    7. Ke Zhu & Shiqing Ling, 2012. "Likelihood ratio tests for the structural change of an AR(p) model to a Threshold AR(p) model," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(2), pages 223-232, March.
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    Cited by:

    1. Tahir Andrabi & Jishnu Das & Asim Ijaz Khwaja, 2015. "Delivering education: a pragmatic framework for improving education in low-income countries," Chapters, in: Pauline Dixon & Steve Humble & Chris Counihan (ed.), Handbook of International Development and Education, chapter 6, pages 85-130, Edward Elgar Publishing.
    2. Ke Zhu & Wai Keung Li & Philip L. H. Yu, 2017. "Buffered Autoregressive Models With Conditional Heteroscedasticity: An Application to Exchange Rates," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(4), pages 528-542, October.

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    More about this item

    Keywords

    AR(p) model; Bootstrap method; Buffered AR(p) model; Likelihood ratio test; Marked empirical process; Threshold AR(p) model.;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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