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Forecasting Random Walks under Drift Instability

  • M. Hashem Pesaran
  • Andreas Pick

This paper considers forecast averaging when the same model is used but estimation is carried out over different estimation windows. It develops theoretical results for random walks when their drift and/or volatility are subject to one or more structural breaks. It is shown that compared to using forecasts based on a single estimation window, averaging over estimation windows leads to a lower bias and to a lower root mean square forecast error for all but the smallest of breaks. Similar results are also obtained when observations are exponentially down-weighted, although in this case the performance of forecasts based on exponential down-weighting critically depends on the choice of the weighting coefficient. The forecasting techniques are applied to 20 weekly series of stock market futures and it is found that average forecasting methods in general perform better than using forecasts based on a single estimation window.��Â

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Paper provided by Netherlands Central Bank, Research Department in its series DNB Working Papers with number 207.

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Date of creation: Mar 2009
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Handle: RePEc:dnb:dnbwpp:207
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  1. Todd E. Clark & Michael W. McCracken, 2009. "Improving Forecast Accuracy By Combining Recursive And Rolling Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 50(2), pages 363-395, 05.
  2. Timmermann, Allan, 2006. "Forecast Combinations," Handbook of Economic Forecasting, Elsevier.
  3. Pesaran, M. Hashem & Timmermann, Allan, 2007. "Selection of estimation window in the presence of breaks," Journal of Econometrics, Elsevier, vol. 137(1), pages 134-161, March.
  4. M. Hashem Pesaran & Til Schuermann & L. Vanessa Smith, 2008. "Forecasting economic and financial variables with global VARs," Staff Reports 317, Federal Reserve Bank of New York.
  5. Todd E. Clark & Michael W. McCracken, 2007. "Averaging forecasts from VARs with uncertain instabilities," Finance and Economics Discussion Series 2007-42, Board of Governors of the Federal Reserve System (U.S.).
  6. Burdekin, Richard C K & Siklos, Pierre L, 1999. "Exchange Rate Regimes and Shifts in Inflation Persistence: Does Nothing Else Matter?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 31(2), pages 235-47, May.
  7. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
  8. Clemen, Robert T., 1989. "Combining forecasts: A review and annotated bibliography," International Journal of Forecasting, Elsevier, vol. 5(4), pages 559-583.
  9. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
  10. Carlos Robalo Marques, 2005. "Inflation persistence: facts or artefacts?," Economic Bulletin and Financial Stability Report Articles, Banco de Portugal, Economics and Research Department.
  11. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-44, January.
  12. Gardner, Everette Jr., 2006. "Exponential smoothing: The state of the art--Part II," International Journal of Forecasting, Elsevier, vol. 22(4), pages 637-666.
  13. Katrin Assenmacher-Wesche & M. Hashem Pesaran, 2008. "Forecasting the Swiss Economy Using VECX* Models: An Exercise in Forecast Combination Across Modelsand Observation Windows," Working Papers 2008-03, Swiss National Bank.
  14. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
  15. Harvey, David & Leybourne, Stephen & Newbold, Paul, 1997. "Testing the equality of prediction mean squared errors," International Journal of Forecasting, Elsevier, vol. 13(2), pages 281-291, June.
  16. Branch, William A. & Evans, George W., 2006. "A simple recursive forecasting model," Economics Letters, Elsevier, vol. 91(2), pages 158-166, May.
  17. Clements, Michael P. & Hendry, David F., 2006. "Forecasting with Breaks," Handbook of Economic Forecasting, Elsevier.
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