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Forecasting Random Walks Under Drift Instability

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  • M. Hashem Pesaran
  • Andreas Pick

Abstract

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 monthly inflation series of 21 OECD countries and it is found that average forecasting methods in general perform better than using forecasts based on a single estimation window.

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Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 2293.

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Date of creation: 2008
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Handle: RePEc:ces:ceswps:_2293

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Keywords: forecast combinations; averaging over estimation windows; exponentially down-weighting observations; structural breaks;

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References

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  1. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(1), pages 134-44, January.
  2. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 9552, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  3. Todd E. Clark & Michael W. McCracken, 2008. "Improving forecast accuracy by combining recursive and rolling forecasts," Working Papers 2008-028, Federal Reserve Bank of St. Louis.
  4. Carlos Robalo Marques, 2005. "Inflation persistence: facts or artefacts?," Economic Bulletin and Financial Stability Report Articles, Banco de Portugal, Economics and Research Department.
  5. Pesaran, M. Hashem & Schuermann, Til & Smith, L. Vanessa, 2009. "Forecasting economic and financial variables with global VARs," International Journal of Forecasting, Elsevier, vol. 25(4), pages 642-675, October.
  6. Todd E. Clark & Michael W. McCracken, 2007. "Averaging forecasts from VARs with uncertain instabilities," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 2007-42, Board of Governors of the Federal Reserve System (U.S.).
  7. Branch, William A. & Evans, George W., 2006. "A simple recursive forecasting model," Economics Letters, Elsevier, vol. 91(2), pages 158-166, May.
  8. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737, 9.
  9. Timmermann, Allan, 2006. "Forecast Combinations," Handbook of Economic Forecasting, Elsevier, Elsevier.
  10. 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.
  11. 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.
  12. BAI, Jushan & PERRON, Pierre, 1998. "Computation and Analysis of Multiple Structural-Change Models," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 9807, Universite de Montreal, Departement de sciences economiques.
  13. Gardner, Everette Jr., 2006. "Exponential smoothing: The state of the art--Part II," International Journal of Forecasting, Elsevier, vol. 22(4), pages 637-666.
  14. Burdekin, R.C.K. & Siklos, P.L., 1997. "Exchange Rate Regimes and Shfts in Inflation Persistence: Does Nothing Else Matter?," Working Papers, Wilfrid Laurier University, Department of Economics 97-2, Wilfrid Laurier University, Department of Economics.
  15. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, Econometric Society, vol. 57(2), pages 357-84, March.
  16. 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.
  17. Clemen, Robert T., 1989. "Combining forecasts: A review and annotated bibliography," International Journal of Forecasting, Elsevier, vol. 5(4), pages 559-583.
  18. Clements, Michael P. & Hendry, David F., 2006. "Forecasting with Breaks," Handbook of Economic Forecasting, Elsevier, Elsevier.
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Cited by:
  1. Eklund, Jana & Kapetanios, George & Price, Simon, 2010. "Forecasting in the presence of recent structural change," Bank of England working papers 406, Bank of England.
  2. Pesaran, M.H. & Schuermann, T. & Smit, L.V., 2008. "Forecasting Economic and Financial Variables with Global VARs," Cambridge Working Papers in Economics 0807, Faculty of Economics, University of Cambridge.

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