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On the Model-Based Interpretation of Filters and the Reliability of Trend-Cycle Estimates

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  • Tommaso Proietti

Abstract

The article explores and illustrates some of the typical trade-offs which arise in designing filters for the measurement of trends and cycles in economic time series, focusing, in particular, on the fundamental trade-off between the reliability of the estimates and the magnitude of the revisions as new observations become available. This assessment is available through a novel model based approach, according to which an important class of highpass and bandpass filters, encompassing the Hodrick-Prescott (HP) filter, are adapted to the particular time series under investigation. Via a suitable decomposition of the innovation process, it is shown that any linear time series with ARIMA representation can be broken down into orthogonal trend and cycle components, for which the class of filters is optimal. The main results then follow from Wiener-Kolmogorov (WK) signal extraction theory, whereas exact finite sample inferences are provided by the Kalman filter and smoother for the relevant state space representation of the decomposition.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Econometric Reviews.

Volume (Year): 28 (2009)
Issue (Month): 1-3 ()
Pages: 186-208

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Handle: RePEc:taf:emetrv:v:28:y:2009:i:1-3:p:186-208

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Related research

Keywords: Bandpass filters; Kalman filter and Smoother; Revisions; Signal extraction;

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References

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  1. Robert J. Hodrick & Edward Prescott, 1981. "Post-War U.S. Business Cycles: An Empirical Investigation," Discussion Papers 451, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Lawrence J. Christiano & Terry J. Fitzgerald, 1999. "The Band pass filter," Working Paper 9906, Federal Reserve Bank of Cleveland.
    • Lawrence J. Christiano & Terry J. Fitzgerald, 2003. "The Band Pass Filter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(2), pages 435-465, 05.
  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. James Morley & Charles Nelson & Eric Zivot, 2002. "Why Are Beveridge-Nelson and Unobserved-Component Decompositions of GDP So Different?," Working Papers UWEC-2002-01, University of Washington, Department of Economics.
  5. Koopman, S.J.M. & Shephard, N. & Doornik, J.A., 1998. "Statistical Algorithms for Models in State Space Using SsfPack 2.2," Discussion Paper 1998-141, Tilburg University, Center for Economic Research.
  6. Michael Artis & Massimiliano Marcellino & Tommaso Proietti, 2003. "Dating the Euro Area Business Cycle," Working Papers 237, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  7. Athanasios Orphanides & Simon van Norden, 1999. "The reliability of output gap estimates in real time," Finance and Economics Discussion Series 1999-38, Board of Governors of the Federal Reserve System (U.S.).
  8. James H. Stock & Mark W. Watson, 2003. "Has the Business Cycle Changed and Why?," NBER Chapters, in: NBER Macroeconomics Annual 2002, Volume 17, pages 159-230 National Bureau of Economic Research, Inc.
  9. 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 231-47, July-Sept.
  10. Pollock, D. S. G., 2000. "Trend estimation and de-trending via rational square-wave filters," Journal of Econometrics, Elsevier, vol. 99(2), pages 317-334, December.
  11. Michael Artis & Massimiliano Marcellino & Tommaso Proietti, 2004. "Dating Business Cycles: A Methodological Contribution with an Application to the Euro Area," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(4), pages 537-565, 09.
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Cited by:
  1. Jaqueson K. Galimberti & Marcelo L. Moura, 2011. "Improving the reliability of real-time Hodrick-Prescott filtering using survey forecasts," Centre for Growth and Business Cycle Research Discussion Paper Series 159, Economics, The Univeristy of Manchester.
  2. Proietti, Tommaso, 2007. "Signal extraction and filtering by linear semiparametric methods," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 935-958, October.
  3. Boriss Siliverstovs, 2013. "Dating Business Cycles in Historical Perspective: Evidence for Switzerland," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), Justus-Liebig University Giessen, Department of Statistics and Economics, vol. 233(5-6), pages 661-679, October.
  4. Tommaso Proietti & Alberto Musso, 2012. "Growth accounting for the euro area," Empirical Economics, Springer, vol. 43(1), pages 219-244, August.
  5. Michal Andrle, 2013. "What Is in Your Output Gap? Unified Framework & Decomposition into Observables," IMF Working Papers 13/105, International Monetary Fund.
  6. Proietti, Tommaso, 2008. "Structural Time Series Models for Business Cycle Analysis," MPRA Paper 6854, University Library of Munich, Germany.

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