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Is the Spurious Regression Problem Spurious?

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  • Bennett T. McCallum

Abstract

So-called "spurious regression" relationships between random-walk (or strongly autoregressive) variables are generally accompanied by clear signs of severe autocorrelation in their residuals. A conscientious researcher would therefore not end an investigation with such a result, but would likely re-estimate with an autocorrelation correction. Simulations show, for several typical cases, that the test-rejection statistics for the re-estimated relationships are very close to the true values, so do not yield results of the spurious type.

Suggested Citation

  • Bennett T. McCallum, 2010. "Is the Spurious Regression Problem Spurious?," NBER Working Papers 15690, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:15690
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    References listed on IDEAS

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    1. Clive Granger & Namwon Hyung & Yongil Jeon, 2001. "Spurious regressions with stationary series," Applied Economics, Taylor & Francis Journals, vol. 33(7), pages 899-904.
    2. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    3. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    4. Bennett T. McCallum, 1993. "Unit roots in macroeconomic time series: some critical issues," Economic Quarterly, Federal Reserve Bank of Richmond, issue Spr, pages 13-44.
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    1. Martínez-Rivera, Berenice & Ventosa-Santaulària, Daniel, 2012. "A comment on ‘Is the spurious regression problem spurious?’," Economics Letters, Elsevier, vol. 115(2), pages 229-231.
    2. Antoni, 2015. "The dynamic relationship between money supply and economic growth," Economic Journal of Emerging Markets, Universitas Islam Indonesia, vol. 7(2), pages 78-92, April.
    3. Sollis, Robert, 2011. "Spurious regression: A higher-order problem," Economics Letters, Elsevier, vol. 111(2), pages 141-143, May.
    4. Jerome Apt & Dennis Epple & Fallaw Sowell, 2023. "Forest Fires: Why The Large Year-to-Year Variation in Forests Burned?," NBER Working Papers 31738, National Bureau of Economic Research, Inc.
    5. Jin, Hao & Zhang, Jinsuo & Zhang, Si & Yu, Cong, 2013. "The spurious regression of AR(p) infinite-variance sequence in the presence of structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 25-40.
    6. Daniel Ventosa-Santaulària & J. Eduardo Vera-Valdés & Alejandra I. Martínez-Olmos, 2016. "A comment on ‘resolving spurious regressions and serially correlated errors’," Empirical Economics, Springer, vol. 51(3), pages 1289-1298, November.
    7. Olivo, Victor, 2023. "Show Me the Money. Why Neglecting Money in Monetary Theory and Policy is a Bad Idea," MPRA Paper 118993, University Library of Munich, Germany, revised 27 Oct 2023.
    8. Tu, Yundong, 2017. "On spurious regressions with partial unit root processes," Economics Letters, Elsevier, vol. 150(C), pages 142-145.
    9. Feng, Zongbao & Chen, Weiya & Liu, Yang & Chen, Hongyu & Skibniewski, Mirosław J., 2023. "Long-term equilibrium relationship analysis and energy-saving measures of metro energy consumption and its influencing factors based on cointegration theory and an ARDL model," Energy, Elsevier, vol. 263(PD).
    10. Grzegorz Zimon & Dulal Chandra Pattak & Liton Chandra Voumik & Salma Akter & Funda Kaya & Robert Walasek & Konrad Kochański, 2023. "The Impact of Fossil Fuels, Renewable Energy, and Nuclear Energy on South Korea’s Environment Based on the STIRPAT Model: ARDL, FMOLS, and CCR Approaches," Energies, MDPI, vol. 16(17), pages 1-21, August.
    11. Zhang, Lingxiang, 2013. "Partial unit root and linear spurious regression: A Monte Carlo simulation study," Economics Letters, Elsevier, vol. 118(1), pages 189-191.
    12. Vyrost, Tomas & Baumöhl, Eduard & Lyocsa, Stefan, 2013. "What Drives the Stock Market Integration in the CEE-3?," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 61(1), pages 67-81.
    13. Rosdiana Sijabat, 2022. "The Association of Economic Growth, Foreign Aid, Foreign Direct Investment and Gross Capital Formation in Indonesia: Evidence from the Toda–Yamamoto Approach," Economies, MDPI, vol. 10(4), pages 1-22, April.
    14. Frédéric Branger, Philippe Quirion, Julien Chevallier, 2017. "Carbon Leakage and Competitiveness of Cement and Steel Industries Under the EU ETS: Much Ado About Nothing," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3).
    15. Gueorgui I. Kolev, 2011. "The "spurious regression problem" in the classical regression model framework," Economics Bulletin, AccessEcon, vol. 31(1), pages 925-937.
    16. Zhang, Lingxiang, 2018. "Spurious regressions with high-order models: A reconsideration," Economics Letters, Elsevier, vol. 168(C), pages 70-72.

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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C29 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Other

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