Pitfalls in the use of Time as an Explanatory Variable in Regression
AbstractRegression of a trendless random walk on time produces R-squared values around .44 regardless of sample length. The residuals from the regression exhibit only about 14 percent as much variation as the original series even though the underlying process has no functional dependence on time. The autocorrelation structure of these "detrended" random walks is pseudo-cyclical and purely artifactual. Conventional tests for trend are strongly biased towards finding a trend when none is present, and this effect is only partially mitigated by Cochrane-Orcutt correction for autocorrelation. The results are extended to show that pairs of detrended random walks exhibit spurious correlation.
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Bibliographic InfoPaper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0030.
Date of creation: Nov 1983
Date of revision:
Publication status: published as Nelson, Charles R. and Heejoon Kang. "Pitfalls in the Use of Time as an Explanatory Variable in Regression," Journal of Business and Economic Statistics, Vol. 2, No. 1, January 1984, pp. 73-82.
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- Nelson, Charles R & Kang, Heejoon, 1984. "Pitfalls in the Use of Time as an Explanatory Variable in Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(1), pages 73-82, January.
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- Nelson, Charles R & Kang, Heejoon, 1979.
"Spurious Periodicity in Inappropriately Detrended Time Series,"
The Warwick Economics Research Paper Series (TWERPS)
161, University of Warwick, Department of Economics.
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- Michael C. Lovell, 1963. "Seasonal Adjustment of Economic Time Series and Multiple Regression," Cowles Foundation Discussion Papers 151, Cowles Foundation for Research in Economics, Yale University.
- Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
- Chan, K Hung & Hayya, Jack C & Ord, J Keith, 1977. "A Note on Trend Removal Methods: The Case of Polynomial Regression versus Variate Differencing," Econometrica, Econometric Society, vol. 45(3), pages 737-44, April.
- Plosser, Charles I. & Schwert, G. William, 1977. "Estimation of a non-invertible moving average process : The case of overdifferencing," Journal of Econometrics, Elsevier, vol. 6(2), pages 199-224, September.
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