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

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Author Info
Charles R. Nelson
Heejoon Kang

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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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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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Handle: RePEc:nbr:nberte:0030

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  1. 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. [Downloadable!] (restricted)
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  3. Nelson, Charles R & Kang, Heejoon, 1981. "Spurious Periodicity in Inappropriately Detrended Time Series," Econometrica, Econometric Society, vol. 49(3), pages 741-51, May. [Downloadable!] (restricted)
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  4. 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. [Downloadable!] (restricted)
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  1. Theodore J. Joyce & Naci H. Mocan, 1993. "Unemployment and Infant Health: Times-Series Evidence from the State of Tennessee," NBER Working Papers 3694, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  2. Marian Berneburg, 2006. "Excess Volatility in European Equity Style Indices - New Evidence," IWH Discussion Papers 16-06, Halle Institute for Economic Research. [Downloadable!]
  3. Robert F. Engle & Joao Victor Issler, 1993. "Estimating Sectoral Cycles Using Cointegration and Common Features," NBER Working Papers 4529, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  4. Butler, L, 1996. "The Bank of Canada's New Quarterly Porjection Model Part 4 : A Semi- Structural Method to Estimate Potential Output : Combining Economic Theory with a Time-Series Filter," Technical Reports 77, Bank of Canada. [Downloadable!]
  5. Goldberg, Linda S., 1989. "Nominal Exchange Rate Petterns: Effects On Entry, Exit And Investment In United States," Working Papers 89-25, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
  6. Ehsan Ahmed & J. Rosser & Richard Sheehan, 1989. "A comparison of national and international aggregate supply and demand var models: The United States, Japan and the European economic community," Review of World Economics (Weltwirtschaftliches Archiv), Springer, vol. 125(2), pages 252-272, June. [Downloadable!] (restricted)
  7. Paul, Catherine J. Morrison, 1999. "Production Structure And Trends In The U.S. Meat And Poultry Products Industries," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 24(02), December. [Downloadable!]
  8. Ardeni, Pier Giorgio & Wright, Brian, 1990. "The long term behavior of commodity prices," Policy Research Working Paper Series 358, The World Bank. [Downloadable!]
  9. Hassan Shirvani & Barry Wilbratte, 1994. "Money And Inflation: International Evidence Based On Cointegration Theory," International Economic Journal, Korean International Economic Association, vol. 8(1), pages 11-21, April. [Downloadable!] (restricted)
  10. Lambert, David K. & Schuck, Eric C. & Jin, Hyun & Koo, Won W., 2003. "The Effects Of Us/Canada Trade On Production Costs And Productivity," 2003 Annual meeting, July 27-30, Montreal, Canada 22008, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association). [Downloadable!]
  11. Heejoon Kang, 1999. "The Applied Cointegration Analysis for the Open Economy: A Critical Review," Open Economies Review, Springer, vol. 10(3), pages 325-346, July. [Downloadable!] (restricted)
  12. Hope Corman & H. Naci Mocan, 2000. "A Time-Series Analysis of Crime, Deterrence, and Drug Abuse in New York City," American Economic Review, American Economic Association, vol. 90(3), pages 584-604, June. [Downloadable!] (restricted)
  13. Qinghua Liu & C. Richard Shumway, 2006. "Geographic aggregation and induced innovation in American agriculture," Applied Economics, Taylor and Francis Journals, vol. 38(6), pages 671-682, April. [Downloadable!] (restricted)
  14. Liu, Qinghua & Shumway, C. Richard, 2003. "Induced Innovation Tests On Western American Agriculture: A Cointegration Analysis," 2003 Annual meeting, July 27-30, Montreal, Canada 22237, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association). [Downloadable!]
  15. Naci H. Mocan, 1991. "Business Cycles and Fertility Dynamics in the U.S.: A Vector-Autoregressive Model," NBER Working Papers 3177, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  16. Heejoon Kang, 2006. "Inappropriate Detrending and Spurious Cointegration," Working Papers 2006-14, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy. [Downloadable!]
    Other versions:
  17. Hope Corman & H. Naci Mocan, 1996. "A Time-Series Analysis of Crime and Drug Use in New York City," NBER Working Papers 5463, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  18. N. Gregory Mankiw & Matthew D. Shapiro, 1985. "Do We Reject Too Often? Small Sample Properties of Tests of Rational Expectations Models," NBER Technical Working Papers 0051, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  19. Linda S. Goldberg, 1990. "Nominal Exchange Rate Patterns: Correlationswith Entry, Exit, and Invesment in U.S. Industry," NBER Working Papers 3249, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  20. Bennett T. McCallum, 1993. "Unit roots in macroeconomic time series: some critical issues," Economic Quarterly, Federal Reserve Bank of Richmond, issue Spr, pages 13-44. [Downloadable!]
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  21. Lavan Mahadeva and Paul Robinson, 2004. "Unit Root Testing in a Central Bank," Handbooks, Centre for Central Banking Studies, Bank of England, number 22, December. [Downloadable!]
  22. Jesus Felipe, Carsten A. Holz, 2001. "Why do Aggregate Production Functions Work? Fisher’s simulations, Shaikh’s identity and some new results," International Review of Applied Economics, Taylor and Francis Journals, vol. 15(3), pages 261-285, July. [Downloadable!] (restricted)
  23. N. Vijayamohanan Pillai, 2001. "Electricity demand analysis and forecasting: The tradition is questioned," Centre for Development Studies, Trivendrum Working Papers 312, Centre for Development Studies, Trivendrum, India. [Downloadable!]
  24. Theodore J. Joyce, 1990. "A Time-Series Analysis of Unemployment and Health: The Case of Birth Outcomes in New York City," NBER Working Papers 2834, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
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