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The Beveridge–Nelson Decomposition: A Different Perspective with New Results

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  • Victor Gomez
  • Jorg Breitung

Abstract

We show that the decomposition proposed by Beveridge and Nelson (J. Monet. Econ. 7 (1981), 151–74) for models that are integrated of order 1 can be generalized to seasonal autoregressive integrated moving‐average models by means of a partial fraction decomposition. An algorithm which is very fast and easy to implement is proposed to optimally (in the mean squared sense) compute the estimates of the components in the generalized decomposition.

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  • Victor Gomez & Jorg Breitung, 1999. "The Beveridge–Nelson Decomposition: A Different Perspective with New Results," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(5), pages 527-535, September.
    • Handle: RePEc:bla:jtsera:v:20:y:1999:i:5:p:527-535
    DOI: 10.1111/1467-9892.00154
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    1. 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.
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    3. 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.
    4. Arnold Zellner, 1978. "Seasonal Analysis of Economic Time Series," NBER Books, National Bureau of Economic Research, Inc, number zell78-1.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
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    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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