Spurious Regression Unmasked
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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- Phillips, P.C.B., 1986.
"Understanding spurious regressions in econometrics,"
Journal of Econometrics,
Elsevier, vol. 33(3), pages 311-340, December.
- Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
- 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.
- 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.
- Hendry, David F, 1980. "Econometrics-Alchemy or Science?," Economica, London School of Economics and Political Science, vol. 47(188), pages 387-406, November.
- Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.