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Unit Root Tests Are Useful for Selecting Forecasting Models

  • Francis X. Diebold
  • Lutz Kilian

We study the usefulness of root tests as diagnostic tools for selecting forecasting models. Difference stationary and trend stationary models of economic and financial time series often imply very different predictions, so deciding which model to use is tremendously important for applied forecasters. Forecasters face three choices: always difference the data, never difference, or use a unit-root pretest. We characterize the predictive loss of these strategies for the canonical AR(1) process with trend, focusing on the effects of sample size, forecast horizon, and degree of persistence. We show that pretesting routinely improves forecast accuracy relative to forecasts from models in differences, and we give conditions under which pretesting is likely to improve forecast accuracy relative to forecasts from models in levels.

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File URL: http://www.nber.org/papers/w6928.pdf
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 6928.

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Date of creation: Feb 1999
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Publication status: published as Diebold, Francis X. and Lutz Kilian. "Unit-Root Tests Are Useful For Selecting Forecasting Models," Journal of Business and Economic Statistics, 2000, v18(3,Jul), 265-273.
Handle: RePEc:nbr:nberwo:6928
Note: EFG AP
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  1. Lawrence J. Christiano & Martin Eichenbaum, 1989. "Unit Roots in Real GNP: Do We Know, and Do We Care?," NBER Working Papers 3130, National Bureau of Economic Research, Inc.
  2. Christoffersen, Peter F & Diebold, Francis X, 1998. "Cointegration and Long-Horizon Forecasting," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(4), pages 450-58, October.
  3. Zivot, Eric & Andrews, Donald W K, 1992. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 251-70, July.
  4. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-36, July.
  5. Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?," Cowles Foundation Discussion Papers 979, Cowles Foundation for Research in Economics, Yale University.
  6. Glenn D. Rudebusch, 1992. "The uncertain unit root in real GNP," Finance and Economics Discussion Series 193, Board of Governors of the Federal Reserve System (U.S.).
  7. Caner, Mehmet & Kilian, Lutz, 1999. "Size distortions of tests of the null hypothesis of stationarity: Evidence and implications for applied work," ZEI Working Papers B 12-1999, ZEI - Center for European Integration Studies, University of Bonn.
  8. Diebold, Francis X & Senhadji, Abdelhak S, 1996. "The Uncertain Unit Root in Real GNP: Comment," American Economic Review, American Economic Association, vol. 86(5), pages 1291-98, December.
  9. John Y. Campbell & Pierre Perron, 1991. "Pitfalls and Opportunities: What Macroeconomists Should Know About Unit Roots," NBER Technical Working Papers 0100, National Bureau of Economic Research, Inc.
  10. Phillips, Peter C.B. & Ploberger, Werner, 1994. "Posterior Odds Testing for a Unit Root with Data-Based Model Selection," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 774-808, August.
  11. Leybourne, S J & McCabe, B P M, 1994. "A Consistent Test for a Unit Root," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 157-66, April.
  12. Michael P. Clements & David F. Hendry, 1999. "On winning forecasting competitions in economics," Spanish Economic Review, Springer, vol. 1(2), pages 123-160.
  13. Lutz Kilian, 1998. "Small-Sample Confidence Intervals For Impulse Response Functions," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 218-230, May.
  14. Ng, S. & Perron, P., 1994. "Unit Root Tests ARMA Models with Data Dependent Methods for the Selection of the Truncation Lag," Cahiers de recherche 9423, Universite de Montreal, Departement de sciences economiques.
  15. James H. Stock & Mark W. Watson, 1998. "A Comparison of Linear and Nonlinear Univariate Models for Forecasting Macroeconomic Time Series," NBER Working Papers 6607, National Bureau of Economic Research, Inc.
  16. Andrews, Donald W K & Chen, Hong-Yuan, 1994. "Approximately Median-Unbiased Estimation of Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 187-204, April.
  17. Eugene Canjels & Mark W. Watson, 1994. "Estimating Deterministic Trends in the Presence of Serially Correlated Errors," NBER Technical Working Papers 0165, National Bureau of Economic Research, Inc.
  18. Franses, Philip Hans & Kleibergen, Frank, 1996. "Unit roots in the Nelson-Plosser data: Do they matter for forecasting?," International Journal of Forecasting, Elsevier, vol. 12(2), pages 283-288, June.
  19. Stock, James H, 1996. "VAR, Error Correction and Pretest Forecasts at Long Horizons," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(4), pages 685-701, November.
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