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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. Weiss, Andrew A., 1991. "Multi-step estimation and forecasting in dynamic models," Journal of Econometrics, Elsevier, Elsevier, vol. 48(1-2), pages 135-149.
  2. James C. Morley & Charles Nelson & Eric Zivot, 2000. "Why Are Beveridge-Nelson and Unobserved-Component Decompositions of GDP So Different?," Discussion Papers in Economics at the University of Washington, Department of Economics at the University of Washington 0013, Department of Economics at the University of Washington.
  3. 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.
  4. Cogley, Timothy, 2002. "A Simple Adaptive Measure of Core Inflation," Journal of Money, Credit and Banking, Blackwell Publishing, Blackwell Publishing, vol. 34(1), pages 94-113, February.
  5. Kum Hwa Oh & Eric Zivot & Drew Creal, 2006. "The Relationship between the Beveridge-Nelson Decomposition andUnobserved Component Models with Correlated Shocks," Working Papers, University of Washington, Department of Economics UWEC-2006-16-FC, University of Washington, Department of Economics.
  6. Charles R. Nelson, 2006. "The Beveridge-Nelson Decomposition in Retrospect and Prospect," Working Papers, University of Washington, Department of Economics UWEC-2007-30, University of Washington, Department of Economics.
  7. Marcellino, Massimiliano & Stock, James H. & Watson, Mark W., 2006. "A comparison of direct and iterated multistep AR methods for forecasting macroeconomic time series," Journal of Econometrics, Elsevier, Elsevier, vol. 135(1-2), pages 499-526.
  8. Brockwell, P. J. & Dahlhaus, R., 2004. "Generalized Levinson-Durbin and Burg algorithms," Journal of Econometrics, Elsevier, Elsevier, vol. 118(1-2), pages 129-149.
  9. Morley, James C., 2002. "A state-space approach to calculating the Beveridge-Nelson decomposition," Economics Letters, Elsevier, Elsevier, vol. 75(1), pages 123-127, March.
  10. Tommaso Proietti, 2006. "Trend-Cycle Decompositions with Correlated Components," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 25(1), pages 61-84.
  11. Ing, Ching-Kang, 2003. "Multistep Prediction In Autoregressive Processes," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 19(02), pages 254-279, April.
  12. 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.
  13. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, Elsevier, vol. 18(1), pages 49-75, July.
  14. Clive W. J. Granger & Yongil Jeon, 2006. "Dynamics of Model Overfitting Measured in terms of Autoregressive Roots," Journal of Time Series Analysis, Wiley Blackwell, Wiley Blackwell, vol. 27(3), pages 347-365, 05.
  15. Guillaume Chevillon, 2005. "Direct multi-step estimation and forecasting," Documents de Travail de l'OFCE, Observatoire Francais des Conjonctures Economiques (OFCE) 2005-10, Observatoire Francais des Conjonctures Economiques (OFCE).
  16. Proietti, Tommaso & Harvey, Andrew, 2000. "A Beveridge-Nelson smoother," Economics Letters, Elsevier, Elsevier, vol. 67(2), pages 139-146, May.
  17. Morley, James C., 2011. "The Two Interpretations Of The Beveridge–Nelson Decomposition," Macroeconomic Dynamics, Cambridge University Press, Cambridge University Press, vol. 15(03), pages 419-439, June.
  18. Clements, Michael P. & Hendry, David F., 1996. "Multi-Step Estimation for Forecasting," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 447, University of Warwick, Department of Economics.
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