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The exact linkage between the Beveridge-Nelson decomposition and other permanent-transitory decompositions
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The exact linkage between the Beveridge-Nelson decomposition and other permanent-transitory decompositions

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  • Giacomo Sbrana

    (BETA/CNRS, Université de Strasbourg, France.)

Abstract

The econometric literature has recently focused attention on the relationship between the Beveridge–Nelson decomposition and unobserved components processes when decomposing time series into permanent and transitory shocks. This paper shows the existence of an algebraic linkage between reduced and structural forms parameters of some unobserved components processes. Results allow measuring how close standard unobserved components processes and unrestricted ARIMA models are regardless of the number of structural/reduced form parameters. Results are provided when the reduced forms are ARIMA(2,1,2) and ARIMA(0,2,2). For the latter, the exact relation between the Hodrick–Prescott filter and the IMA(2,2) reduced form is also shown.
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Suggested Citation

  • Giacomo Sbrana, 2010. "The exact linkage between the Beveridge-Nelson decomposition and other permanent-transitory decompositions," Working Papers 10-09, Association Française de Cliométrie (AFC).
    • Handle: RePEc:afc:wpaper:10-09
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    References listed on IDEAS

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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.
    2. 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.
    3. Zarnowitz, Victor & Ozyildirim, Ataman, 2006. "Time series decomposition and measurement of business cycles, trends and growth cycles," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1717-1739, October.
    4. Oh, Kum Hwa & Zivot, Eric & Creal, Drew, 2008. "The relationship between the Beveridge-Nelson decomposition and other permanent-transitory decompositions that are popular in economics," Journal of Econometrics, Elsevier, vol. 146(2), pages 207-219, October.
    5. Harvey, A C, 1985. "Trends and Cycles in Macroeconomic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(3), pages 216-227, June.
    6. Peter K. Clark, 1987. "The Cyclical Component of U. S. Economic Activity," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(4), pages 797-814.
    7. Tommaso Proietti, 2006. "Trend-Cycle Decompositions with Correlated Components," Econometric Reviews, Taylor & Francis Journals, vol. 25(1), pages 61-84.
    8. 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.
    9. 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.
    10. Kum Hwa Oh & Eric Zivot, 2006. "The Clark Model with Correlated Components," Working Papers UWEC-2006-06, University of Washington, Department of Economics.
    11. Maravall, A. & del Rio, A., 2007. "Temporal aggregation, systematic sampling, and the Hodrick-Prescott filter," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 975-998, October.
    12. Harvey, A C & Jaeger, A, 1993. "Detrending, Stylized Facts and the Business Cycle," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(3), pages 231-247, July-Sept.
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    Cited by:

    1. Murasawa, Yasutomo, 2015. "The multivariate Beveridge–Nelson decomposition with I(1) and I(2) series," Economics Letters, Elsevier, vol. 137(C), pages 157-162.
    2. Riccardo De Bonis & Andrea Silvestrini, 2014. "The Italian financial cycle: 1861-2011," Cliometrica, Journal of Historical Economics and Econometric History, Association Française de Cliométrie (AFC), vol. 8(3), pages 301-334, September.

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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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