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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. 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. Yoichi Ueno, 2024. "Linkage between Wage and Price Inflation in Japan," Bank of Japan Working Paper Series 24-E-7, Bank of Japan.
    12. Travaglini, Guido, 2010. "Dynamic Econometric Testing of Climate Change and of its Causes," MPRA Paper 23600, University Library of Munich, Germany.
    13. D. Ventosa-Santaulària, 2009. "Spurious Regression," Journal of Probability and Statistics, Hindawi, vol. 2009, pages 1-27, August.
    14. 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.
    15. 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.
    16. Phillips, Peter C.B. & Kheifets, Igor L., 2024. "High-dimensional IV cointegration estimation and inference," Journal of Econometrics, Elsevier, vol. 238(2).
    17. 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.
    18. 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.
    19. 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.
    20. Shintani, Mototsugu & Yabu, Tomoyoshi & Nagakura, Daisuke, 2012. "Spurious regressions in technical trading," Journal of Econometrics, Elsevier, vol. 169(2), pages 301-309.
    21. 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.
    22. Gueorgui I. Kolev, 2011. "The "spurious regression problem" in the classical regression model framework," Economics Bulletin, AccessEcon, vol. 31(1), pages 925-937.
    23. repec:wyi:journl:002191 is not listed on IDEAS

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