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The Multistep Beveridge-Nelson Decomposition

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  • Tommaso Proietti

Abstract

The Beveridge-Nelson decomposition defines the trend component in terms of the eventual forecast function, as the value the series would take if it were on its long-run path. The paper in-troduces the multistep Beveridge-Nelson decomposition, which arises when the forecast function is obtained by the direct autoregressive approach, which optimizes the predictive ability of the AR model at forecast horizons greater than one. We compare our proposal with the standard Beveridge-Nelson decomposition, for which the forecast function is obtained by iterating the one-step-ahead predictions via the chain rule. We illustrate that the multistep Beveridge-Nelson trend is more efficient than the standard one in the presence of model misspecification and we subsequently assess the predictive validity of the extracted transitory component with respect to future growth.

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Paper provided by Economics and Econometrics Research Institute (EERI), Brussels in its series EERI Research Paper Series with number EERI_RP_2009_24.

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Date of creation: 09 2009
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Handle: RePEc:eei:rpaper:eeri_rp_2009_24

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Keywords: Trend and Cycle; Forecasting; Filtering.;

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  1. Tommaso Proietti, 2006. "Trend-Cycle Decompositions with Correlated Components," Econometric Reviews, Taylor & Francis Journals, vol. 25(1), pages 61-84.
  2. Charles Nelson & Eric Zivot, 2000. "Why are Beveridge-Nelson and Unobserved-Component Decompositions of GDP so Different?," Econometric Society World Congress 2000 Contributed Papers 0692, Econometric Society.
  3. Cogley, Timothy, 2002. "A Simple Adaptive Measure of Core Inflation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 34(1), pages 94-113, February.
  4. Kum Hwa Oh & Eric Zivot & Drew Creal, 2006. "The Relationship between the Beveridge-Nelson Decomposition andUnobserved Component Models with Correlated Shocks," Working Papers UWEC-2006-16-FC, University of Washington, Department of Economics.
  5. Clements, Michael P & Hendry, David F, 1996. "Multi-step Estimation for Forecasting," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(4), pages 657-84, November.
  6. Ing, Ching-Kang, 2003. "Multistep Prediction In Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 19(02), pages 254-279, April.
  7. Clive W. J. Granger & Yongil Jeon, 2006. "Dynamics of Model Overfitting Measured in terms of Autoregressive Roots," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(3), pages 347-365, 05.
  8. Nelson, Charles R., 2008. "The Beveridge-Nelson decomposition in retrospect and prospect," Journal of Econometrics, Elsevier, vol. 146(2), pages 202-206, October.
  9. Morley, James C., 2011. "The Two Interpretations Of The Beveridge–Nelson Decomposition," Macroeconomic Dynamics, Cambridge University Press, vol. 15(03), pages 419-439, June.
  10. James H. Stock & Mark W. Watson, 2006. "Why Has U.S. Inflation Become Harder to Forecast?," NBER Working Papers 12324, National Bureau of Economic Research, Inc.
  11. Weiss, Andrew A., 1991. "Multi-step estimation and forecasting in dynamic models," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 135-149.
  12. Morley, James C., 2002. "A state-space approach to calculating the Beveridge-Nelson decomposition," Economics Letters, Elsevier, vol. 75(1), pages 123-127, March.
  13. Massimiliano Marcellino & James Stock & Mark Watson, 2005. "A Comparison of Direct and Iterated Multistep AR Methods for Forecasting Macroeconomic Time Series," Working Papers 285, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  14. James C. Morley & Charles R. Nelson & Eric Zivot, 2003. "Why Are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP So Different?," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 235-243, May.
  15. Proietti, Tommaso & Harvey, Andrew, 2000. "A Beveridge-Nelson smoother," Economics Letters, Elsevier, vol. 67(2), pages 139-146, May.
  16. Guillaume Chevillon, 2005. "Direct multi-step estimation and forecasting," Documents de Travail de l'OFCE 2005-10, Observatoire Francais des Conjonctures Economiques (OFCE).
  17. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July.
  18. Brockwell, P. J. & Dahlhaus, R., 2004. "Generalized Levinson-Durbin and Burg algorithms," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 129-149.
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