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Pitfalls in the use of Time as an Explanatory Variable in Regression

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  • Charles R. Nelson
  • Heejoon Kang

Abstract

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.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0030.

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Date of creation: Nov 1983
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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.
Handle: RePEc:nbr:nberte:0030

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  1. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, Elsevier, vol. 2(2), pages 111-120, July.
  2. 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, Econometric Society, vol. 45(3), pages 737-44, April.
  3. Nelson, Charles R & Kang, Heejoon, 1979. "Spurious Periodicity in Inappropriately Detrended Time Series," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 161, University of Warwick, Department of Economics.
  4. Plosser, Charles I. & Schwert, G. William, 1977. "Estimation of a non-invertible moving average process : The case of overdifferencing," Journal of Econometrics, Elsevier, Elsevier, vol. 6(2), pages 199-224, September.
  5. 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, Elsevier, vol. 10(1), pages 113-163, January.
  6. Michael C. Lovell, 1963. "Seasonal Adjustment of Economic Time Series and Multiple Regression," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 151, Cowles Foundation for Research in Economics, Yale University.
  7. Durbin, J, 1970. "Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors are Lagged Dependent Variables," Econometrica, Econometric Society, Econometric Society, vol. 38(3), pages 410-21, May.
  8. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, Elsevier, vol. 10(2), pages 139-162.
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