IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/1330.html
   My bibliography  Save this paper

Bootstrapping Spurious Regression

Author

Abstract

The bootstrap is shown to be inconsistent in spurious regression. The failure of the bootstrap is spectacular in that the bootstrap effectively turns a spurious regression into a cointegrating regression. In particular, the serial correlation coefficient of the residuals in the bootstrap regression does not converge to unity, so the bootstrap is not even first order consistent. The block bootstrap serial correlation coefficient does converge to unity and is therefore first order consistent, but has a slower rate of convergence and a different limit distribution from that of the sample data serial correlation coefficient. The analysis covers spurious regressions involving both deterministic trends and stochastic trends. The results reinforce earlier warnings about routine use of the bootstrap with dependent data.

Suggested Citation

  • Peter C.B. Phillips, 2001. "Bootstrapping Spurious Regression," Cowles Foundation Discussion Papers 1330, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1330
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d13/d1330.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hinkley, D. V., 1997. "Discussion of paper by H. Li & G.S. Maddala," Journal of Econometrics, Elsevier, vol. 80(2), pages 319-323, October.
    2. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    3. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    4. Horowitz, Joel L., 1999. "The Bootstrap," Working Papers 99-10, University of Iowa, Department of Economics.
    5. Phillips, Peter C B & Ploberger, Werner, 1996. "An Asymptotic Theory of Bayesian Inference for Time Series," Econometrica, Econometric Society, vol. 64(2), pages 381-412, March.
    6. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
    7. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
    8. Phillips, Peter C.B., 2007. "Unit root log periodogram regression," Journal of Econometrics, Elsevier, vol. 138(1), pages 104-124, May.
    9. Li, Hongyi & Maddala, G. S., 1997. "Bootstrapping cointegrating regressions," Journal of Econometrics, Elsevier, vol. 80(2), pages 297-318, October.
    10. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    11. Park, Joon Y., 2002. "An Invariance Principle For Sieve Bootstrap In Time Series," Econometric Theory, Cambridge University Press, vol. 18(2), pages 469-490, April.
    12. Durlauf, Steven N & Phillips, Peter C B, 1988. "Trends versus Random Walks in Time Series Analysis," Econometrica, Econometric Society, vol. 56(6), pages 1333-1354, November.
    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. Phillips, Peter C.B., 2010. "Bootstrapping I(1) data," Journal of Econometrics, Elsevier, vol. 158(2), pages 280-284, October.
    2. Imed Drine & Christophe Rault, 2008. "Purchasing Power Parity For Developing And Developed Countries. What Can We Learn From Non‐Stationary Panel Data Models?," Journal of Economic Surveys, Wiley Blackwell, vol. 22(4), pages 752-773, September.
    3. Banerjee, Anindya & Carrion-i-Silvestre, Josep Lluís, 2006. "Cointegration in panel data with breaks and cross-section dependence," Working Paper Series 591, European Central Bank.
    4. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Carsten Jentsch & Dimitris N. Politis & Efstathios Paparoditis, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 416-441, May.
    5. Burridge, Peter & Robert Taylor, A. M., 2004. "Bootstrapping the HEGY seasonal unit root tests," Journal of Econometrics, Elsevier, vol. 123(1), pages 67-87, November.
    6. Jentsch, Carsten & Paparoditis, Efstathios & Politis, Dimitris N., 2014. "Block Bootstrap Theory for Multivariate Integrated and Cointegrated Processes," Working Papers 14-18, University of Mannheim, Department of Economics.

    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. Peter C. B. Phillips, 2021. "Pitfalls in Bootstrapping Spurious Regression," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 163-217, December.
    2. Phillips, Peter C. B., 2002. "New unit root asymptotics in the presence of deterministic trends," Journal of Econometrics, Elsevier, vol. 111(2), pages 323-353, December.
    3. Peter C. B. Phillips, 2003. "Laws and Limits of Econometrics," Economic Journal, Royal Economic Society, vol. 113(486), pages 26-52, March.
    4. Ziwei Mei & Zhentao Shi & Peter C. B. Phillips, 2022. "The boosted HP filter is more general than you might think," Cowles Foundation Discussion Papers 2348, Cowles Foundation for Research in Economics, Yale University.
    5. Peter C. B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-470, December.
    6. Ibragimov, Rustam & Phillips, Peter C.B., 2008. "Regression Asymptotics Using Martingale Convergence Methods," Econometric Theory, Cambridge University Press, vol. 24(4), pages 888-947, August.
    7. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
    8. Peter C. B. Phillips & Xiaohu Wang & Yonghui Zhang, 2019. "HAR Testing for Spurious Regression in Trend," Econometrics, MDPI, vol. 7(4), pages 1-28, December.
    9. Peter C.B. Phillips & Zhipeng Liao, 2012. "Series Estimation of Stochastic Processes: Recent Developments and Econometric Applications," Cowles Foundation Discussion Papers 1871, Cowles Foundation for Research in Economics, Yale University.
    10. Cheng, Xu & Phillips, Peter C.B., 2012. "Cointegrating rank selection in models with time-varying variance," Journal of Econometrics, Elsevier, vol. 169(2), pages 155-165.
    11. Jürgen Wolters & Uwe Hassler, 2006. "Unit root testing," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 90(1), pages 43-58, March.
    12. Jentsch, Carsten & Paparoditis, Efstathios & Politis, Dimitris N., 2014. "Block Bootstrap Theory for Multivariate Integrated and Cointegrated Processes," Working Papers 14-18, University of Mannheim, Department of Economics.
    13. Joon Y. Park, 2003. "Bootstrap Unit Root Tests," Econometrica, Econometric Society, vol. 71(6), pages 1845-1895, November.
    14. Peter C. B. Phillips & Sainan Jin, 2021. "Business Cycles, Trend Elimination, And The Hp Filter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(2), pages 469-520, May.
    15. Phillips, Peter C.B., 2010. "Bootstrapping I(1) data," Journal of Econometrics, Elsevier, vol. 158(2), pages 280-284, October.
    16. Peter C. B. Phillips, 2001. "Descriptive econometrics for non-stationary time series with empirical illustrations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 389-413.
    17. Peter C.B. Phillips, 1994. "Nonstationary Time Series and Cointegration: Recent Books and Themes for the Future," Cowles Foundation Discussion Papers 1081, Cowles Foundation for Research in Economics, Yale University.
    18. Joakim Westerlund, 2005. "New Simple Tests for Panel Cointegration," Econometric Reviews, Taylor & Francis Journals, vol. 24(3), pages 297-316.
    19. Pesavento, Elena, 2004. "Analytical evaluation of the power of tests for the absence of cointegration," Journal of Econometrics, Elsevier, vol. 122(2), pages 349-384, October.
    20. Peter C.B. Phillips & Tassos Magadalinos, 2005. "Limit Theory for Moderate Deviations from a Unit Root under Weak Dependence," Cowles Foundation Discussion Papers 1517, Cowles Foundation for Research in Economics, Yale University.

    More about this item

    Keywords

    Asymptotic theory; Bootstrap; Brownian motion; Cointegration; LK representation; Nonstationarity; Residual diagnostics; Unit root;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:cwl:cwldpp:1330. 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: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.html .

    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.