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Spurious Relationships for Nearly Non-Stationary Series

Author

Listed:
  • Yushan Cheng

    (School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China)

  • Yongchang Hui

    (School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China)

  • Michael McAleer

    (Department of Finance, College of Management, Asia University, Taichung City 41354, Taiwan
    Department of Bioinformatics and Medical Engineering, College of Information and Electrical Engineering, Asia University, Taichung City 41354, Taiwan
    Discipline of Business Analytics, University of Sydney Business School, Darlington, NSW 2006, Australia
    Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam, 3062 PA Rotterdam, The Netherlands)

  • Wing-Keung Wong

    (Department of Finance, Fintech and Blockchain Research Center, and Big Data Research Center, Asia University, 500, Lioufeng Road, Wufeng, Taichung City 41354, Taiwan
    Department of Medical Research, China Medical University Hospital, Taichung City 41354, Taiwan
    Department of Economics and Finance, The Hang Seng University of Hong Kong, Siu Lek Yuen, Hong Kong, China)

Abstract

Literature shows that the regression of independent and (nearly) nonstationary time series could result in spurious outcomes. In this paper, we conjecture that under some situations, the regression of two independent and nearly non-stationary series does not have any spurious problem at all. To check whether our conjecture holds, we set up several situations and conduct simulations to justify our conjecture. Our simulations show that under some situations, the chance that the regressions being spurious is very high for all the cases simulated in our paper. Nonetheless, under some other situations, our simulation shows that the rejection rates are much smaller than the 5% level of significance for all the cases simulated in our paper, implying that our conjecture could hold under some situations that regression of two independent and nearly non-stationary series does not have any spurious problem at all.

Suggested Citation

  • Yushan Cheng & Yongchang Hui & Michael McAleer & Wing-Keung Wong, 2021. "Spurious Relationships for Nearly Non-Stationary Series," JRFM, MDPI, vol. 14(8), pages 1-24, August.
    • Handle: RePEc:gam:jjrfmx:v:14:y:2021:i:8:p:366-:d:610705
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    References listed on IDEAS

    as
    1. Smith, Richard J. & Taylor, A.M. Robert & del Barrio Castro, Tomas, 2009. "Regression-Based Seasonal Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 25(2), pages 527-560, April.
    2. M. L. Tiku & Wing‐Keung Wong & David C. Vaughan & Guorui Bian, 2000. "Time Series Models in Non‐Normal Situations: Symmetric Innovations," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(5), pages 571-596, September.
    3. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    4. Castro, Tomás del Barrio & Osborn, Denise R. & Taylor, A.M. Robert, 2012. "On Augmented Hegy Tests For Seasonal Unit Roots," Econometric Theory, Cambridge University Press, vol. 28(5), pages 1121-1143, October.
    5. Tomás del Barrio Castro & Gianluca Cubadda & Denise R. Osborn, 2022. "On cointegration for processes integrated at different frequencies," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 412-435, May.
    6. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
    7. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    8. Wong, Wing-Keung & Bian, Guorui, 2005. "Estimating parameters in autoregressive models with asymmetric innovations," Statistics & Probability Letters, Elsevier, vol. 71(1), pages 61-70, January.
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