Advanced Search
MyIDEAS: Login

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

Contents:

Author Info

  • Tommaso Proietti

    (University of Udine)

Abstract

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.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://128.118.178.162/eps/em/papers/0403/0403007.pdf
Download Restriction: no

Bibliographic Info

Paper provided by EconWPA in its series Econometrics with number 0403007.

as in new window
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://128.118.178.162

Related research

Keywords: Signal Extraction; Revisions; Kalman filter and Smoother.;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. Athanasios Orphanides & Simon van Norden, 2001. "The Unreliability of Output Gap Estimates in Real Time," CIRANO Working Papers 2001s-57, CIRANO.
  6. 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.
  7. 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.
  8. Artis, Michael J & Marcellino, Massimiliano & Proietti, Tommaso, 2003. "Dating the Euro Area Business Cycle," CEPR Discussion Papers 3696, C.E.P.R. Discussion Papers.
  9. 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.
  10. 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.
  11. 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.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Tommaso Proietti, 2008. "Structural Time Series Models for Business Cycle Analysis," CEIS Research Paper 109, Tor Vergata University, CEIS, revised 10 Jul 2008.
  2. Tommaso Proietti & Alberto Musso, 2012. "Growth accounting for the euro area," Empirical Economics, Springer, vol. 43(1), pages 219-244, August.
  3. Proietti, Tommaso, 2007. "Signal extraction and filtering by linear semiparametric methods," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 935-958, October.
  4. 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.
  5. Michal Andrle, 2013. "What Is in Your Output Gap? Unified Framework & Decomposition into Observables," IMF Working Papers 13/105, International Monetary Fund.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpem:0403007. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.