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A Convergent t-statistic in Spurious Regressions

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  • Sun, Yixiao

Abstract

This paper proposes a convergent t-statistic for spurious regressions. The new t-statistic is based on the heteroscedasiticity and autocorrelation consistent (HAC) standard error estimate with the bandwidth equal to the sample size. Using autocovariances of all lags, the so-defined HAC estimator is capable of capturing the high persistence of the regressor and regression residuals. It is shown that the new t-statistic converges to a non-degenerate limiting distribution for all cases of spurious regressions considered in the literature. This finding suggests that inferences based on the new t-statistic and asymptotic theory developed in this paper will not result in the finding of a significant relationship that does not actually exist.

Suggested Citation

  • Sun, Yixiao, 2003. "A Convergent t-statistic in Spurious Regressions," University of California at San Diego, Economics Working Paper Series qt150457tv, Department of Economics, UC San Diego.
  • Handle: RePEc:cdl:ucsdec:qt150457tv
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    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. 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.
    3. 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.
    4. 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.
    5. Antonio E. Noriega & Daniel Ventosa-Santaulària, 2011. "A Simple Test for Spurious Regressions," Working Papers 2011-05, Banco de México.
    6. Mototsugu Shintani & Tomoyoshi Yabu & and 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.
    7. 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.
    8. Ventosa-Santaulària, Daniel, 2008. "Spurious Regression," MPRA Paper 59008, University Library of Munich, Germany.
    9. Shintani, Mototsugu & Yabu, Tomoyoshi & Nagakura, Daisuke, 2012. "Spurious regressions in technical trading," Journal of Econometrics, Elsevier, vol. 169(2), pages 301-309.
    10. Sun, Yixiao, 2014. "Fixed-smoothing Asymptotics and Asymptotic F and t Tests in the Presence of Strong Autocorrelation," University of California at San Diego, Economics Working Paper Series qt8479f4s2, Department of Economics, UC San Diego.
    11. 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.
    12. Gueorgui I. Kolev, 2011. "The "spurious regression problem" in the classical regression model framework," Economics Bulletin, AccessEcon, vol. 31(1), pages 925-937.
    13. Travaglini, Guido, 2010. "Dynamic Econometric Testing of Climate Change and of its Causes," MPRA Paper 23600, University Library of Munich, Germany.
    14. repec:wyi:journl:002191 is not listed on IDEAS

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