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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.

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File URL: http://cowles.econ.yale.edu/P/cd/d11a/d1135.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, 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: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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  1. Steven N. Durlauf & Peter C.B. Phillips, 1986. "Trends Versus Random Walks in Time Series Analysis," Cowles Foundation Discussion Papers 788, Cowles Foundation for Research in Economics, Yale University.
  2. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
  3. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
  4. Hendry, David F, 1980. "Econometrics-Alchemy or Science?," Economica, London School of Economics and Political Science, vol. 47(188), pages 387-406, November.
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Cited by:
  1. 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).
  2. Peter C.B. Phillips, 2004. "HAC Estimation by Automated Regression," Cowles Foundation Discussion Papers 1470, Cowles Foundation for Research in Economics, Yale University.

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