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Trend-Cycle Decompositions with Correlated Components

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  • Tommaso Proietti

Abstract

This paper raises some interpretative issues that arise from univariate trend-cycle decompositions with correlated disturbances. In particular, it discusses whether the interpretation of a negative correlation as providing evidence for the prominence of real, or supply, shocks, can be supported. For this purpose it determines the conditions under which correlated components may originate from the underestimation of the cyclical component in an orthogonal decomposition; from the presence of a growth rate cycle, rather than a deviation cycle; or alternatively, as a consequence of the hysteresis phenomenon. Finally, it considers interpreting correlated components in terms of permanent-transitory decompositions, where the permanent component has richer dynamics than a pure random walk. The consequences for smoothing and signal extraction are discussed: in particular, it is documented that a negative correlation implies that future observations carry most of the information needed to assess cyclical stance. As a result, the components will be subject to underestimation in real time and thus to high revisions. The overall conclusion is that the characterization of economic fluctuations in macroeconomic time series largely remains an open issue.

Suggested Citation

  • Tommaso Proietti, 2006. "Trend-Cycle Decompositions with Correlated Components," Econometric Reviews, Taylor & Francis Journals, vol. 25(1), pages 61-84.
    • Handle: RePEc:taf:emetrv:v:25:y:2006:i:1:p:61-84
    DOI: 10.1080/07474930500545496
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    1. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, Decembrie.
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    1. Kum Hwa Oh & Eric Zivot & Drew Creal, 2006. "The Relationship between the Beveridge-Nelson Decomposition andUnobserved Component Models with Correlated Shocks," Working Papers UWEC-2006-16-FC, University of Washington, Department of Economics.
    2. Sbrana, Giacomo, 2013. "The exact linkage between the Beveridge–Nelson decomposition and other permanent-transitory decompositions," Economic Modelling, Elsevier, vol. 30(C), pages 311-316.
    3. Tommaso Proietti & Alessandra Luati, 2013. "Maximum likelihood estimation of time series models: the Kalman filter and beyond," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 15, pages 334-362, Edward Elgar Publishing.
    4. Breitung, Jörg & Hafner, Christian M., 2016. "A simple model for now-casting volatility series," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1247-1255.
    5. Tommaso Proietti, 2016. "The Multistep Beveridge--Nelson Decomposition," Econometric Reviews, Taylor & Francis Journals, vol. 35(3), pages 373-395, March.
    6. Andrle, Michal, 2008. "The Role of Trends and Detrending in DSGE Models," MPRA Paper 13289, University Library of Munich, Germany.
    7. Emilio Congregado & Antonio Golpe & Simon Parker, 2012. "The dynamics of entrepreneurship: hysteresis, business cycles and government policy," Empirical Economics, Springer, vol. 43(3), pages 1239-1261, December.
    8. Villegas, Marco A. & Pedregal, Diego J., 2019. "Automatic selection of unobserved components models for supply chain forecasting," International Journal of Forecasting, Elsevier, vol. 35(1), pages 157-169.
    9. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2015. "Wave function method to forecast foreign currencies exchange rates at ultra high frequency electronic trading in foreign currencies exchange markets," MPRA Paper 67470, University Library of Munich, Germany.
    10. Mardi Dungey & Jan P.A.M. Jacobs & Jing Tian, 2017. "Forecasting output gaps in the G-7 countries: the role of correlated innovations and structural breaks," Applied Economics, Taylor & Francis Journals, vol. 49(45), pages 4554-4566, September.
    11. Max Soloschenko & Enzo Weber, 2021. "Trend-Cycle Interactions and the Subprime Crisis: Analysis of US and Canadian Output," Journal of Business Cycle Research, Springer;Centre for International Research on Economic Tendency Surveys (CIRET), vol. 17(2), pages 109-128, November.
    12. repec:dgr:rugsom:12009-eef is not listed on IDEAS
    13. Philippe Moës, 2012. "Multivariate models with dual cycles: implications for output gap and potential growth measurement," Empirical Economics, Springer, vol. 42(3), pages 791-818, June.
    14. Attfield, Cliff & Temple, Jonathan R.W., 2010. "Balanced growth and the great ratios: New evidence for the US and UK," Journal of Macroeconomics, Elsevier, vol. 32(4), pages 937-956, December.
    15. M. Dungey & J. P. A. M. Jacobs & J. Tian & S. van Norden, 2013. "On the correspondence between data revision and trend-cycle decomposition," Applied Economics Letters, Taylor & Francis Journals, vol. 20(4), pages 316-319, March.
    16. 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).
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2013. "On the Stratonovich – Kalman - Bucy filtering algorithm application for accurate characterization of financial time series with use of state-space model by central banks," MPRA Paper 50235, University Library of Munich, Germany.
    22. Congregado, Emilio & Golpe, Antonio A. & Carmona, Mónica, 2012. "Looking for hysteresis in coal consumption in the US," Renewable and Sustainable Energy Reviews, Elsevier, vol. 16(5), pages 3339-3343.
    23. Irma Hindrayanto & Jan Jacobs & Denise Osborn, 2014. "On trend-cycle-seasonal interactions," DNB Working Papers 417, Netherlands Central Bank, Research Department.
    24. 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.
    25. Tommaso Proietti & Alessandra Luati, 2013. "Generalised Linear Spectral Models," CEIS Research Paper 290, Tor Vergata University, CEIS, revised 03 Oct 2013.

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