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Spurious Regression Unmasked

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Abstract

This paper argues that trending time series can admit valid regression representations even when the dependent variable and the regressors are statistically independent, i.e., in situations that are presently characterized in the literature as "spurious regressions." Our theory is directed mainly at the two classic examples of regressions of stochastic trends on time polynomials and regressions among independent random walks. But it has more general applicability and, we think, wider implications. Contrary to established wisdom, our theory justifies regressions of this type as valid models for the data. The radical conclusion that emerges from this study is that there are no spurious regressions for trending time series, just alternative valid representations of the limiting dependent variable process in terms of other stochastic processes and deterministic functions of time. We find statistical inference in such cases to be valid, not spurious, a conclusion that is in direct contrast to universal thinking about this subject since Yule (1926) first wrote about nonsense correlations.

Suggested Citation

  • Peter C.B. Phillips, 1996. "Spurious Regression Unmasked," Cowles Foundation Discussion Papers 1135, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1135
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d11/d1135.pdf
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    References listed on IDEAS

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    1. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    2. Durlauf, Steven N & Phillips, Peter C B, 1988. "Trends versus Random Walks in Time Series Analysis," Econometrica, Econometric Society, vol. 56(6), pages 1333-1354, November.
    3. repec:bla:econom:v:47:y:1980:i:188:p:387-406 is not listed on IDEAS
    4. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
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    Cited by:

    1. Dimitrios D. Thomakos, 2008. "Optimal Linear Filtering, Smoothing and Trend Extraction for Processes with Unit Roots and Cointegration," Working Paper series 14_08, Rimini Centre for Economic Analysis.
    2. Phillips, Peter C.B., 2005. "Hac Estimation By Automated Regression," Econometric Theory, Cambridge University Press, vol. 21(1), pages 116-142, February.
    3. Chi-Young Choi & Ling Hu & Masao Ogaki, 2005. "Structural Spurious Regressions and A Hausman-type Cointegration Test," RCER Working Papers 517, University of Rochester - Center for Economic Research (RCER).
    4. 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.
    5. Schmidt, Anatoly B., 2009. "Detrending the realized volatility in the global FX market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(9), pages 1887-1892.

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