Pitfalls in the use of Time as an Explanatory Variable in Regression
Regression 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.
|Date of creation:||Nov 1983|
|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.|
|Contact details of provider:|| Postal: National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.|
Web page: http://www.nber.org
More information through EDIRC
References listed on IDEAS
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.:
- 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 737-744, 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.
- 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.
- Nelson, Charles R & Kang, Heejoon, 1981.
"Spurious Periodicity in Inappropriately Detrended Time Series,"
Econometric Society, vol. 49(3), pages 741-751, May.
- 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.
- Durbin, J, 1970. "Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors are Lagged Dependent Variables," Econometrica, Econometric Society, vol. 38(3), pages 410-421, May.
- Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
- Perloff, Jeffrey M. & Wachter, Michael L., 1979. "A production function--nonaccelerating inflation approach to potential output : Is measured potential output too high?," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 10(1), pages 113-163, January.
- 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.
When requesting a correction, please mention this item's handle: RePEc:nbr:nberte:0030. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.