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Spurious Regression Unmasked

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Author Info
Peter C.B. Phillips () (Cowles Foundation, Yale University)

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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.

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File URL: http://cowles.econ.yale.edu/P/cd/d11a/d1135.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1135.

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Length: 38 pages
Date of creation: Oct 1996
Date of revision:
Handle: RePEc:cwl:cwldpp:1135

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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  1. Durlauf, Steven N & Phillips, Peter C B, 1988. "Trends versus Random Walks in Time Series Analysis," Econometrica, Econometric Society, vol. 56(6), pages 1333-54, November. [Downloadable!] (restricted)
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  2. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December. [Downloadable!] (restricted)
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  3. Hendry, David F, 1980. "Econometrics-Alchemy or Science?," Economica, London School of Economics and Political Science, vol. 47(188), pages 387-406, November. [Downloadable!] (restricted)
  4. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Dimitrios Thomakos, 2008. "Optimal Linear Filtering, Smoothing and Trend Extraction for Processes with Unit Roots and Cointegration," Working Papers 0024, University of Peloponnese, Department of Economics. [Downloadable!]
    Other versions:
  2. Peter C.B. Phillips, 2004. "HAC Estimation by Automated Regression," Cowles Foundation Discussion Papers 1470, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  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). [Downloadable!]
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