IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v20y2004i05p943-962_20.html
   My bibliography  Save this article

A CONVERGENT t-STATISTIC IN SPURIOUS REGRESSIONS

Author

Listed:
  • Sun, Yixiao

Abstract

This paper investigates the asymptotic properties of the t-statistic in spurious regressions when the bandwidth in the estimation of the heteroskedasticity and autocorrelation consistent (HAC) standard error is set proportional to the sample size. Using autocovariances of large lags, the so-defined HAC estimator is capable of capturing the high persistence of the regressor and regression residuals. It is shown that the resulting t-statistic converges to a nondegenerate limiting distribution for all cases of spurious regressions considered in the literature. This finding sheds some new light on the nature of spurious regressions.I am very grateful to Bruce Hansen and two anonymous referees for helpful comments and suggestions. All remaining errors and omissions are mine alone.

Suggested Citation

  • Sun, Yixiao, 2004. "A CONVERGENT t-STATISTIC IN SPURIOUS REGRESSIONS," Econometric Theory, Cambridge University Press, vol. 20(5), pages 943-962, October.
    • Handle: RePEc:cup:etheor:v:20:y:2004:i:05:p:943-962_20
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0266466604205072/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Other versions of this item:

    Citations

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


    Cited by:

    1. Sun, Yixiao, 2006. "Spurious regressions between stationary generalized long memory processes," Economics Letters, Elsevier, vol. 90(3), pages 446-454, March.
    2. Peter C.B. Phillips & Igor Kheifets, 2021. "On Multicointegration," Cowles Foundation Discussion Papers 2306, Cowles Foundation for Research in Economics, Yale University.
    3. Fabrizio Iacone & Stephen J. Leybourne & A. M. Robert Taylor, 2014. "A FIXED- b TEST FOR A BREAK IN LEVEL AT AN UNKNOWN TIME UNDER FRACTIONAL INTEGRATION," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(1), pages 40-54, January.
    4. Noriega Antonio E. & Ventosa-Santaulària Daniel, 2011. "A Simple Test for Spurious Regressions," Working Papers 2011-05, Banco de México.
    5. Kong, Jianning & Phillips, Peter C.B. & Sul, Donggyu, 2019. "Weak σ-convergence: Theory and applications," Journal of Econometrics, Elsevier, vol. 209(2), pages 185-207.
    6. McElroy, Tucker & Politis, Dimitris N., 2013. "Distribution theory for the studentized mean for long, short, and negative memory time series," Journal of Econometrics, Elsevier, vol. 177(1), pages 60-74.
    7. Capucine Nobletz, 2021. "Return spillovers between green energy indexes and financial markets: a first sectoral approach," EconomiX Working Papers 2021-24, University of Paris Nanterre, EconomiX.
    8. Lui, Yiu Lim & Phillips, Peter C.B. & Yu, Jun, 2024. "Robust testing for explosive behavior with strongly dependent errors," Journal of Econometrics, Elsevier, vol. 238(2).
    9. Pellatt, Daniel F. & Sun, Yixiao, 2023. "Asymptotic F test in regressions with observations collected at high frequency over long span," Journal of Econometrics, Elsevier, vol. 235(2), pages 1281-1309.
    10. Yixiao Sun, 2014. "Fixed-smoothing Asymptotics and AsymptoticFandtTests in the Presence of Strong Autocorrelation," Advances in Econometrics, in: Essays in Honor of Peter C. B. Phillips, volume 14, pages 23-63, Emerald Group Publishing Limited.
    11. Travaglini, Guido, 2010. "Dynamic Econometric Testing of Climate Change and of its Causes," MPRA Paper 23600, University Library of Munich, Germany.
    12. D. Ventosa-Santaulària, 2009. "Spurious Regression," Journal of Probability and Statistics, Hindawi, vol. 2009, pages 1-27, August.
    13. Xu, Ke-Li, 2016. "Multivariate trend function testing with mixed stationary and integrated disturbances," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 38-57.
    14. Ghouse, Ghulam & Khan, Saud Ahmed & Rehman, Atiq Ur, 2018. "ARDL model as a remedy for spurious regression: problems, performance and prospectus," MPRA Paper 83973, University Library of Munich, Germany.
    15. 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.
    16. Christophe Boucher & Gilles de Truchis & Elena Ivona Dumitrescu & Sessi Tokpavi, 2017. "Testing for Extreme Volatility Transmission with Realized Volatility Measures," Working Papers hal-04141651, HAL.
    17. Mototsugu Shintani & Tomoyoshi Yabu & Daisuke Nagakura, 2008. "Spurious Regressions in Technical Trading: Momentum or Contrarian?," IMES Discussion Paper Series 08-E-09, Institute for Monetary and Economic Studies, Bank of Japan.
    18. Shintani, Mototsugu & Yabu, Tomoyoshi & Nagakura, Daisuke, 2012. "Spurious regressions in technical trading," Journal of Econometrics, Elsevier, vol. 169(2), pages 301-309.
    19. Christophe Boucher & Gilles de Truchis & Elena Dumitrescu & Sessi Tokpavi, 2017. "Testing for Extreme Volatility Transmission with Realized Volatility Measures," EconomiX Working Papers 2017-20, University of Paris Nanterre, EconomiX.
    20. Gueorgui I. Kolev, 2011. "The "spurious regression problem" in the classical regression model framework," Economics Bulletin, AccessEcon, vol. 31(1), pages 925-937.
    21. repec:wyi:journl:002191 is not listed on IDEAS

    More about this item

    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:cup:etheor:v:20:y:2004:i:05:p:943-962_20. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/ect .

    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.