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

  • Tommaso Proietti

    (University of Udine)

The paper is concerned with a class of trend cycle filters, encompassing popular ones, such as the Hodrick-Prescott filter, that are derived using the Wiener-Kolmogorov signal extraction theory under maintained models that prove unrealistic in applied time series analysis. As the maintained model is misspecified, inference about the unobserved components, and in particular their first two conditional moments, given the observations, are not delivered by the Kalman filter and smoother or the Wiener-Kolmogorov filter for the maintained model. The paper proposes a model based framework according to which the same class of filters is 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. Finite sample inferences are provided by the Kalman filter and smoother for the relevant state space representation of the decomposition. In this framework it is possible to discuss two aspects of the reliability of the signals’ estimates: the mean square error of the final estimates and the extent of the revisions. The paper discusses and illustrates how the uncertainty is related to features of the series and the design parameters of the filter, the role of smoothness priors, and the fundamental trade-off between the uncertainty and the magnitude of the revisions as new observations become available.

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File URL: http://econwpa.repec.org/eps/em/papers/0403/0403007.pdf
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Paper provided by EconWPA in its series Econometrics with number 0403007.

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Length: 25 pages
Date of creation: 18 Mar 2004
Date of revision:
Handle: RePEc:wpa:wuwpem:0403007
Note: Type of Document - pdf; pages: 25
Contact details of provider: Web page: http://econwpa.repec.org

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  1. 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.
  2. 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.
  3. Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 107-160.
  4. 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.).
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
  10. Michael ARTIS & Massimiliano MARCELLINO & Tommaso PROIETTI, 2002. "Dating the Euro Area Business Cycle," Economics Working Papers ECO2002/24, European University Institute.
  11. Marianne Baxter & Robert G. King, 1995. "Measuring Business Cycles Approximate Band-Pass Filters for Economic Time Series," NBER Working Papers 5022, National Bureau of Economic Research, Inc.
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