IDEAS home Printed from https://ideas.repec.org/a/eee/ecolet/v172y2018icp123-126.html
   My bibliography  Save this article

Threshold regression asymptotics: From the compound Poisson process to two-sided Brownian motion

Author

Listed:
  • Yu, Ping
  • Phillips, Peter C.B.

Abstract

The asymptotic distribution of the least squares estimator in threshold regression is expressed in terms of a compound Poisson process when the threshold effect is fixed and as a functional of two-sided Brownian motion when the threshold effect shrinks to zero. This paper explains the relationship between this dual limit theory by showing how the asymptotic forms are linked in terms of joint and sequential limits. In one case, joint asymptotics apply when both the sample size diverges and the threshold effect shrinks to zero, whereas sequential asymptotics operate in the other case in which the sample size diverges first and the threshold effect shrinks subsequently. The two operations lead to the same limit distribution, thereby linking the two different cases. The proofs make use of ideas involving limit theory for sums of a random number of summands.

Suggested Citation

  • Yu, Ping & Phillips, Peter C.B., 2018. "Threshold regression asymptotics: From the compound Poisson process to two-sided Brownian motion," Economics Letters, Elsevier, vol. 172(C), pages 123-126.
    • Handle: RePEc:eee:ecolet:v:172:y:2018:i:c:p:123-126
    DOI: 10.1016/j.econlet.2018.08.039
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165176518303604
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econlet.2018.08.039?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    2. Anna Bykhovskaya & Peter C. B. Phillips, 2018. "Boundary Limit Theory for Functional Local to Unity Regression," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(4), pages 523-562, July.
    3. Jushan Bai, 1997. "Estimation Of A Change Point In Multiple Regression Models," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 551-563, November.
    4. Yu, Ping, 2012. "Likelihood estimation and inference in threshold regression," Journal of Econometrics, Elsevier, vol. 167(1), pages 274-294.
    5. Yu, Ping, 2014. "The Bootstrap In Threshold Regression," Econometric Theory, Cambridge University Press, vol. 30(3), pages 676-714, June.
    6. Ping Yu & Yongqiang Zhao, 2013. "Asymptotics for threshold regression under general conditions," Econometrics Journal, Royal Economic Society, vol. 16(3), pages 430-462, October.
    7. Peter C. B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Econometrica, Econometric Society, vol. 67(5), pages 1057-1112, September.
    8. Yu, Ping, 2015. "Adaptive estimation of the threshold point in threshold regression," Journal of Econometrics, Elsevier, vol. 189(1), pages 83-100.
    9. James Heckman, 1997. "Instrumental Variables: A Study of Implicit Behavioral Assumptions Used in Making Program Evaluations," Journal of Human Resources, University of Wisconsin Press, vol. 32(3), pages 441-462.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chaoyi Chen & Thanasis Stengos, 2022. "Estimation and Inference for the Threshold Model with Hybrid Stochastic Local Unit Root Regressors," JRFM, MDPI, vol. 15(6), pages 1-15, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yu, Ping & Phillips, Peter C.B., 2018. "Threshold regression with endogeneity," Journal of Econometrics, Elsevier, vol. 203(1), pages 50-68.
    2. Yu, Ping, 2015. "Adaptive estimation of the threshold point in threshold regression," Journal of Econometrics, Elsevier, vol. 189(1), pages 83-100.
    3. Daniel J. Henderson & Christopher F. Parmeter & Liangjun Su, 2017. "M-Estimation of a Nonparametric Threshold Regression Model," Working Papers 2017-15, University of Miami, Department of Economics.
    4. Lee, Yoonseok & Wang, Yulong, 2023. "Threshold regression with nonparametric sample splitting," Journal of Econometrics, Elsevier, vol. 235(2), pages 816-842.
    5. Porter, Jack & Yu, Ping, 2015. "Regression discontinuity designs with unknown discontinuity points: Testing and estimation," Journal of Econometrics, Elsevier, vol. 189(1), pages 132-147.
    6. Ping Yu & Shengjie Hong & Peter C. B. Phillips, 2022. "Panel Threshold Regression with Unobserved Individual-Specific Threshold Effects," Cowles Foundation Discussion Papers 2352, Cowles Foundation for Research in Economics, Yale University.
    7. Koo, Bonsoo & Seo, Myung Hwan, 2015. "Structural-break models under mis-specification: Implications for forecasting," Journal of Econometrics, Elsevier, vol. 188(1), pages 166-181.
    8. Alastair R. Hall & Denise R. Osborn & Nikolaos Sakkas, 2017. "The asymptotic behaviour of the residual sum of squares in models with multiple break points," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 667-698, October.
    9. Kourtellos, Andros & Stengos, Thanasis & Sun, Yiguo, 2022. "Endogeneity In Semiparametric Threshold Regression," Econometric Theory, Cambridge University Press, vol. 38(3), pages 562-595, June.
    10. Baltagi, Badi H. & Feng, Qu & Kao, Chihwa, 2016. "Estimation of heterogeneous panels with structural breaks," Journal of Econometrics, Elsevier, vol. 191(1), pages 176-195.
    11. Badi H. Baltagi & Chihwa Kao & Long Liu, 2017. "Estimation and identification of change points in panel models with nonstationary or stationary regressors and error term," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 85-102, March.
    12. Kapetanios, George & Mitchell, James & Shin, Yongcheol, 2014. "A nonlinear panel data model of cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 179(2), pages 134-157.
    13. Miao, Ke & Su, Liangjun & Wang, Wendun, 2020. "Panel threshold regressions with latent group structures," Journal of Econometrics, Elsevier, vol. 214(2), pages 451-481.
    14. Donayre Luiggi & Eo Yunjong & Morley James, 2018. "Improving likelihood-ratio-based confidence intervals for threshold parameters in finite samples," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(1), pages 1-11, February.
    15. Markus Eberhardt & Francis Teal, 2011. "Econometrics For Grumblers: A New Look At The Literature On Cross‐Country Growth Empirics," Journal of Economic Surveys, Wiley Blackwell, vol. 25(1), pages 109-155, February.
    16. Adhvaryu, Achyuta & Fenske, James & Khanna, Gaurav & Nyshadham, Anant, 2021. "Resources, conflict, and economic development in Africa," Journal of Development Economics, Elsevier, vol. 149(C).
    17. repec:wyi:journl:002203 is not listed on IDEAS
    18. Fitzpatrick, Luke & Parmeter, Christopher F. & Agar, Juan, 2017. "Threshold Effects in Meta-Analyses With Application to Benefit Transfer for Coral Reef Valuation," Ecological Economics, Elsevier, vol. 133(C), pages 74-85.
    19. Kourtellos, Andros & Stengos, Thanasis & Tan, Chih Ming, 2016. "Structural Threshold Regression," Econometric Theory, Cambridge University Press, vol. 32(4), pages 827-860, August.
    20. Spenkuch, Jörg, 2013. "On the Extent of Strategic Voting," MPRA Paper 50198, University Library of Munich, Germany.
    21. Dawei Lu & Yi Ding & Sobhan Asian & Sanjoy Kumar Paul, 2018. "From Supply Chain Integration to Operational Performance: The Moderating Effect of Market Uncertainty," Global Journal of Flexible Systems Management, Springer;Global Institute of Flexible Systems Management, vol. 19(1), pages 3-20, March.

    More about this item

    Keywords

    Threshold regression; Sequential asymptotics; Doob’s martingale inequality; Compound Poisson process; Brownian motion;
    All these keywords.

    JEL classification:

    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecolet:v:172:y:2018:i:c:p:123-126. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ecolet .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.