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Interpretation of the Effects of Filtering Integrated Time Series

  • Valle e Azevedo, João

We resort to a rigorous definition of spectrum of an integrated time series in order to characterise the implications of applying linear filters to such series. We conclude that in the presence of integrated series the transfer function of the filters has exactly the same interpretation as in the covariance stationary case, contrary to what many authors suggest. This disagreement leads to different conclusions regarding the link of the original fluctuations with the transformed fluctuations in the time series data, embodied in various unjustified criticisms to the application of detrending filters. Despite this, and given the frequency domain characteristics of filtered macroeconomic integrated series, we acknowledge that the choice of a particular detrending filter is far from being a neutral task.

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File URL: http://mpra.ub.uni-muenchen.de/6574/1/MPRA_paper_6574.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 6574.

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Date of creation: 21 Sep 2007
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Handle: RePEc:pra:mprapa:6574
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  1. 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. Timothy Cogley & James M. Nason, 1991. "Effects of the Hodrick-Prescott filter on integrated time series," Proceedings, Federal Reserve Bank of San Francisco, issue Nov.
  3. 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.
  4. Canova, Fabio, 1993. "Detrending and Business Cycle Facts," CEPR Discussion Papers 782, C.E.P.R. Discussion Papers.
  5. 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.
  6. King, R.G. & Rebelo, S.T., 1989. "Low Frequency Filtering And Real Business Cycles," RCER Working Papers 205, University of Rochester - Center for Economic Research (RCER).
  7. Valle e Azevedo, João, 2007. "Exact Limit of the Expected Periodogram in the Unit-Root Case," MPRA Paper 6553, University Library of Munich, Germany.
  8. Regina Kaiser & Agustín Maravall, 1999. "Estimation of the Business Cycle: a Modified Hodrick-Prescott Filter," Banco de Espa�a Working Papers 9912, Banco de Espa�a.
  9. Alain GUAY & Pierre SAINT-AMANT, 2005. "Do the Hodrick-Prescott and Baxter-King Filters Provide a Good Approximation of Business Cycles?," Annales d'Economie et de Statistique, ENSAE, issue 77, pages 133-155.
  10. Christian J. Murray, 2003. "Cyclical Properties of Baxter-King Filtered Time Series," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 472-476, May.
  11. Gomez, Victor, 2001. "The Use of Butterworth Filters for Trend and Cycle Estimation in Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(3), pages 365-73, July.
  12. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
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