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The Beveridge-Nelson decomposition: A different perspective with new results

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  • Gómez, Víctor
  • Breitung, Jörg

Abstract

We show in the paper that the decomposition proposed by Beveridge and Nelson (1981) for models that are integrated of order one can be generalized to seasonal Arima models by means of a partial fraction decomposition. Two equivalent algorithms are proposed to optimally (in the mean squared sense) compute the estimates of the components in the generalized decomposition. While the first algorithm is very fast and easy to implement, the second can also provide the standard errors of the estimated components. The properties of the implied filters are investigated and compared with those obtained using the model-based TRAMO/SEATS software package. The alternative methods are applied to the German unemployment series.

Suggested Citation

  • Gómez, Víctor & Breitung, Jörg, 1998. "The Beveridge-Nelson decomposition: A different perspective with new results," SFB 373 Discussion Papers 1998,26, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:199826
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    References listed on IDEAS

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    1. Arnold Zellner, 1978. "Seasonal Analysis of Economic Time Series," NBER Books, National Bureau of Economic Research, Inc, number zell78-1, March.
    2. William Bell & Steven Hillmer, 1991. "Initializing The Kalman Filter For Nonstationary Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 12(4), pages 283-300, July.
    3. Victor Gómez & Agustín Maravall, 1996. "Programs TRAMO and SEATS, Instruction for User (Beta Version: september 1996)," Working Papers 9628, Banco de España.
    4. 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, vol. 7(2), pages 151-174.
    5. Marianne Baxter & Robert G. King, 1999. "Measuring Business Cycles: Approximate Band-Pass Filters For Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 575-593, November.
    6. Agustin Maravall & David A. Pierce, 1987. "A Prototypical Seasonal Adjustment Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(2), pages 177-193, March.
    7. Nerlove, Marc & Grether, David M. & Carvalho, José L., 1979. "Analysis of Economic Time Series," Elsevier Monographs, Elsevier, edition 1, number 9780125157506 edited by Shell, Karl.
    8. Newbold, Paul, 1990. "Precise and efficient computation of the Beveridge-Nelson decomposition of economic time series," Journal of Monetary Economics, Elsevier, vol. 26(3), pages 453-457, December.
    9. Harvey, A C & Todd, P H J, 1983. "Forecasting Economic Time Series with Structural and Box-Jenkins Models: A Case Study," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(4), pages 299-307, October.
    10. Harvey, A C & Todd, P H J, 1983. "Forecasting Economic Time Series with Structural and Box-Jenkins Models: A Case Study: Response," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(4), pages 313-315, October.
    11. Cuddington, John T. & Winters, L. Alan, 1987. "The Beveridge-Nelson decomposition of economic time series : A quick computational method," Journal of Monetary Economics, Elsevier, vol. 19(1), pages 125-127, January.
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    Cited by:

    1. Lacroix, R., 2008. "Analyse conjoncturelle de données brutes et estimation de cycles Partie 1 : estimation et tests," Working papers 209, Banque de France.

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