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The Relationship between the Beveridge-Nelson Decomposition andUnobserved Component Models with Correlated Shocks

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Author Info

  • Kum Hwa Oh

    (Bank of Korea)

  • Eric Zivot

    (University of Washington)

  • Drew Creal

    (Free University Amsterdam)

Abstract

Many researchers believe that the Beveridge-Nelson decomposition leads to permanent and transitory components whose shocks are perfectly negatively correlated. Indeed, some even consider it to be a property of the decomposition. We demonstrate that the Beveridge-Nelson decomposition does not provide definitive information about the correlation between permanent and transitory shocks in an unobserved components model. Given an ARIMA model describing the evolution of U.S. real GDP, we show that there are many state space representations that generate the Beveridge-Nelson decomposition. These include unobserved components models with perfectly correlated shocks and partially correlated shocks. In our applications, the only knowledge we have about the correlation is that it lies in a restricted interval that does not include zero. Although the filtered estimates of the trend and cycle are identical for models with different correlations, the observationally equivalent unobserved components models produce different smoothed estimates.

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Bibliographic Info

Paper provided by University of Washington, Department of Economics in its series Working Papers with number UWEC-2006-16-FC.

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Date of creation: Jul 2006
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Publication status: Forthcoming in JOURNAL OF ECONOMETRICS
Handle: RePEc:udb:wpaper:uwec-2006-16-fc

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References

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  1. Kum Hwa Oh & Eric Zivot, 2006. "The Clark Model with Correlated Components," Working Papers, University of Washington, Department of Economics UWEC-2006-06, University of Washington, Department of Economics.
  2. Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 107-160.
  3. Harvey, A.C. & Koopman, S.J.M., 1999. "Signal Extraction and the Formulation of Unobserved Components Models," Discussion Paper, Tilburg University, Center for Economic Research 1999-44, Tilburg University, Center for Economic Research.
  4. Tommaso Proietti, 2006. "Trend-Cycle Decompositions with Correlated Components," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 25(1), pages 61-84.
  5. Danny Quah, 1991. "The Relative Importance of Permanent and Transitory Components: Identi- fication and Some Theoretical Bounds," NBER Technical Working Papers 0106, National Bureau of Economic Research, Inc.
  6. Gomez, Victor, 2001. "The Use of Butterworth Filters for Trend and Cycle Estimation in Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 19(3), pages 365-73, July.
  7. Heather M. Anderson & Chin Nam Low & Ralph Snyder, 2004. "Single Source of Error State Space Approach to the Beveridge Nelson Decomposition," Monash Econometrics and Business Statistics Working Papers, Monash University, Department of Econometrics and Business Statistics 21/04, Monash University, Department of Econometrics and Business Statistics.
  8. Proietti, Tommaso & Harvey, Andrew, 2000. "A Beveridge-Nelson smoother," Economics Letters, Elsevier, vol. 67(2), pages 139-146, May.
  9. Thomas M. Trimbur, 2006. "Properties of higher order stochastic cycles," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 1-17, 01.
  10. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, Elsevier, vol. 18(1), pages 49-75, July.
  11. 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.
  12. Harvey, A C & Jaeger, A, 1993. "Detrending, Stylized Facts and the Business Cycle," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 8(3), pages 231-47, July-Sept.
  13. Campbell, John & Mankiw, Gregory, 1987. "Are Output Fluctuations Transitory?," Scholarly Articles 3122545, Harvard University Department of Economics.
  14. James C. Morley & Charles Nelson & Eric Zivot, 2000. "Why Are Beveridge-Nelson and Unobserved-Component Decompositions of GDP So Different?," Working Papers, University of Washington, Department of Economics 0013, University of Washington, Department of Economics.
  15. Newbold, Paul, 1990. "Precise and efficient computation of the Beveridge-Nelson decomposition of economic time series," Journal of Monetary Economics, Elsevier, Elsevier, vol. 26(3), pages 453-457, December.
  16. Andrew C. Harvey & Thomas M. Trimbur, 2003. "General Model-Based Filters for Extracting Cycles and Trends in Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 244-255, May.
  17. Matthew D. Shapiro & Mark W. Watson, 1988. "Sources of Business Cycle Fluctuations," Cowles Foundation Discussion Papers 870, Cowles Foundation for Research in Economics, Yale University.
  18. Cuddington, John T. & Winters, L. Alan, 1987. "The Beveridge-Nelson decomposition of economic time series : A quick computational method," Journal of Monetary Economics, Elsevier, Elsevier, vol. 19(1), pages 125-127, January.
  19. Ord, J.K. & Koehler, A. & Snyder, R.D., 1995. "Estimation and Prediction for a Class of Dynamic Nonlinear Statistical Models," Monash Econometrics and Business Statistics Working Papers, Monash University, Department of Econometrics and Business Statistics 4/95, Monash University, Department of Econometrics and Business Statistics.
  20. George Evans & Lucrezia Reichlin, 1994. "Information, forecasts and measurement of the business cycle," ULB Institutional Repository 2013/10155, ULB -- Universite Libre de Bruxelles.
  21. Clark, Peter K, 1987. "The Cyclical Component of U.S. Economic Activity," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 102(4), pages 797-814, November.
  22. Morley, James C., 2002. "A state-space approach to calculating the Beveridge-Nelson decomposition," Economics Letters, Elsevier, vol. 75(1), pages 123-127, March.
  23. Lippi, Marco & Reichlin, Lucrezia, 1992. "On persistence of shocks to economic variables : A common misconception," Journal of Monetary Economics, Elsevier, Elsevier, vol. 29(1), pages 87-93, February.
  24. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, Elsevier, vol. 7(2), pages 151-174.
  25. Gomez, Victor, 1999. "Three Equivalent Methods for Filtering Finite Nonstationary Time Series," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 17(1), pages 109-16, January.
  26. Harvey,Andrew & Koopman,Siem Jan & Shephard,Neil (ed.), 2004. "State Space and Unobserved Component Models," Cambridge Books, Cambridge University Press, number 9780521835954, 9.
  27. Arino, Miguel A. & Newbold, Paul, 1998. "Computation of the Beveridge-Nelson decomposition for multivariate economic time series," Economics Letters, Elsevier, vol. 61(1), pages 37-42, October.
  28. Daisuke Nagakura & Eric Zivot, 2007. "Implications of Two Measures of Persistence for Correlation Between Permanent and Transitory Shocks in U.S. Real GDP," Working Papers, University of Washington, Department of Economics UWEC-2007-07, University of Washington, Department of Economics.
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Cited by:
  1. Proietti, Tommaso, 2011. "The Multistep Beveridge-Nelson Decomposition," Working Papers 1 OMEWP, University of Sydney Business School, Discipline of Business Analytics.

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