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 InfoArticle provided by American Statistical Association in its journal Journal of Business and Economic Statistics.
Volume (Year): 2 (1984)
Issue (Month): 1 (January)
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Other versions of this item:
- Charles R. Nelson & Heejoon Kang, 1983. "Pitfalls in the use of Time as an Explanatory Variable in Regression," NBER Technical Working Papers 0030, National Bureau of Economic Research, Inc.
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.:
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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.
- Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
- 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.
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