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

  • Tommaso Proietti

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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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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  1. Lawrence J. Christiano & Terry J. Fitzgerald, 1999. "The Band Pass Filter," NBER Working Papers 7257, National Bureau of Economic Research, Inc.
    • 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.
  2. 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.
  3. 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.
  4. 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.
  5. Michael ARTIS & Massimiliano MARCELLINO & Tommaso PROIETTI, 2002. "Dating the Euro Area Business Cycle," Economics Working Papers ECO2002/24, European University Institute.
  6. James C. Morley & Charles Nelson & Eric Zivot, 2000. "Why Are Beveridge-Nelson and Unobserved-Component Decompositions of GDP So Different?," Discussion Papers in Economics at the University of Washington 0013, Department of Economics at the University of Washington.
  7. 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.
  8. 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.
  9. Athanasios Orphanides & Simon van Norden, 2002. "The Unreliability of Output-Gap Estimates in Real Time," The Review of Economics and Statistics, MIT Press, vol. 84(4), pages 569-583, November.
  10. 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.
  11. Neil Shephard & Jurgen Doornik & Siem Jan Koopman, 1998. "Statistical algorithms for models in state space using SsfPack 2.2," Economics Series Working Papers 1998-W06, University of Oxford, Department of Economics.
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