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Unit Root Tests are Useful for Selecting Forecasting Models

  • Francis X. Diebold
  • Lutz Kilian

We study the usefulness of unit 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. We consider three strategies: 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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Paper provided by New York University, Leonard N. Stern School of Business- in its series New York University, Leonard N. Stern School Finance Department Working Paper Seires with number 99-063.

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Date of creation: 18 Jan 1999
Date of revision:
Handle: RePEc:fth:nystfi:99-063
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U.S.A.; New York University, Leonard N. Stern School of Business, Department of Economics . 44 West 4th Street. New York, New York 10012-1126

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  1. Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992. "Efficient Tests for an Autoregressive Unit Root," NBER Technical Working Papers 0130, National Bureau of Economic Research, Inc.
  2. 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.
  3. Rudebusch, Glenn D, 1993. "The Uncertain Unit Root in Real GNP," American Economic Review, American Economic Association, vol. 83(1), pages 264-72, March.
  4. 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.
  5. 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.
  6. Mehmet Caner & Lutz Kilian, 1999. "Size Distortions of Tests of the Null Hypothesis of Stationarity: Evidence and Implications for Applied Work," Computing in Economics and Finance 1999 511, Society for Computational Economics.
  7. 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.
  8. Eugene Canjels & Mark W. Watson, 1997. "Estimating Deterministic Trends In The Presence Of Serially Correlated Errors," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 184-200, May.
  9. Campbell, J.Y. & Perron, P., 1991. "Pitfalls and Opportunities: What Macroeconomics should know about unit roots," Papers 360, Princeton, Department of Economics - Econometric Research Program.
  10. 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.
  11. 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.
  12. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
  13. 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.
  14. 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.
  15. 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.
  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. 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.
  18. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "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?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
  19. Michael P. Clements & David F. Hendry, 1999. "On winning forecasting competitions in economics," Spanish Economic Review, Springer;Spanish Economic Association, vol. 1(2), pages 123-160.
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