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The relationship between the Beveridge-Nelson decomposition and other permanent-transitory decompositions that are popular in economics

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  • Oh, Kum Hwa
  • Zivot, Eric
  • Creal, Drew

Abstract

The Beveridge-Nelson (BN) decomposition is a model-based method for decomposing time series into permanent and transitory components. When constructed from an ARIMA model, it is closely related to decompositions based on unobserved components (UC) models with random walk trends and covariance stationary cycles. The decomposition when extended to I(2) models can also be related to non-model-based signal extraction filters such as the HP filter. We show that the BN decomposition provides information on the correlation between the permanent and transitory shocks in a certain class of UC models. The correlation between components is known to determine the smoothed estimates of components from UC models. The BN decomposition can also be used to evaluate the efficacy of alternative methods. We also demonstrate, contrary to popular belief, that the BN decomposition can produce smooth cycles if the reduced form forecasting model is appropriately specified.

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  • 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.
    • Handle: RePEc:eee:econom:v:146:y:2008:i:2:p:207-219
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    Cited by:

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    6. Xu, Zhiwei, 2008. "Univariate Unobserved-Component Model with Non-Random Walk Permanent Component," MPRA Paper 46162, University Library of Munich, Germany.
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    9. Robert Dixon & G. C. Lim, 2013. "A univariate model of aggregate labour productivity," Applied Economics, Taylor & Francis Journals, vol. 45(18), pages 2695-2695, June.
    10. Dungey, Mardi & Jacobs, Jan & Tian, Jing & Norden, Simon van, 2012. "On trend-cycle decomposition and data revision," Research Report 12009-EEF, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    11. Luis Uzeda, 2022. "State Correlation and Forecasting: A Bayesian Approach Using Unobserved Components Models," Advances in Econometrics, in: Essays in Honour of Fabio Canova, volume 44, pages 25-53, Emerald Group Publishing Limited.
    12. Tommaso Proietti, 2021. "Predictability, real time estimation, and the formulation of unobserved components models," Econometric Reviews, Taylor & Francis Journals, vol. 40(5), pages 433-454, April.
    13. Hartl, Tobias, 2021. "Monitoring the pandemic: A fractional filter for the COVID-19 contact rate," VfS Annual Conference 2021 (Virtual Conference): Climate Economics 242380, Verein für Socialpolitik / German Economic Association.
    14. Mardi Dungey & Jan P.A.M. Jacobs & Jing Jian & Simon van Norden, 2013. "Trend-Cycle Decomposition: Implications from an Exact Structural Identification," CIRANO Working Papers 2013s-23, CIRANO.
    15. James Morley & Irina B. Panovska & Tara M. Sinclair, 2014. "Testing Stationarity for Unobserved Components Models," Discussion Papers 2012-41B, School of Economics, The University of New South Wales.
    16. Tobias Hartl & Rolf Tschernig & Enzo Weber, 2020. "Fractional trends and cycles in macroeconomic time series," Papers 2005.05266, arXiv.org, revised May 2020.
    17. Murasawa, Yasutomo, 2015. "The multivariate Beveridge–Nelson decomposition with I(1) and I(2) series," Economics Letters, Elsevier, vol. 137(C), pages 157-162.
    18. Sbrana, Giacomo & Silvestrini, Andrea, 2023. "The RWDAR model: A novel state-space approach to forecasting," International Journal of Forecasting, Elsevier, vol. 39(2), pages 922-937.
    19. Xu, Zhiwei, 2008. "Univariate Unobserved-Component Model with a Non-Random-Walk Permanent Component," MPRA Paper 50053, University Library of Munich, Germany.
    20. Murasawa Yasutomo, 2022. "Bayesian multivariate Beveridge–Nelson decomposition of I(1) and I(2) series with cointegration," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 26(3), pages 387-415, June.
    21. Boz, Emine & Daude, Christian & Bora Durdu, C., 2011. "Emerging market business cycles: Learning about the trend," Journal of Monetary Economics, Elsevier, vol. 58(6), pages 616-631.
    22. Han, Yang & Liu, Zehao & Ma, Jun, 2020. "Growth cycles and business cycles of the Chinese economy through the lens of the unobserved components model," China Economic Review, Elsevier, vol. 63(C).
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