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Interpretation of the Effects of Filtering Integrated Time Series

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  • João Valle e Azevedo

Abstract

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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Paper provided by Banco de Portugal, Economics and Research Department in its series Working Papers with number w200712.

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Date of creation: 2007
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Handle: RePEc:ptu:wpaper:w200712

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  1. Canova, Fabio, 1993. "Detrending and Business Cycle Facts," CEPR Discussion Papers 782, C.E.P.R. Discussion Papers.
  2. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, Blackwell Publishing, vol. 29(1), pages 1-16, February.
  3. Timothy Cogley & James M. Nason, 1991. "Effects of the Hodrick-Prescott filter on integrated time series," Proceedings, Federal Reserve Bank of San Francisco, Federal Reserve Bank of San Francisco, issue Nov.
  4. Harvey, A C & Jaeger, A, 1993. "Detrending, Stylized Facts and the Business Cycle," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 8(3), pages 231-47, July-Sept.
  5. 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.
  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. Alain Guay & Pierre St-Amant, 1997. "Do the Hodrick-Prescott and Baxter-King Filters Provide a Good Approximation of Business Cycles?," Cahiers de recherche CREFE / CREFE Working Papers, CREFE, Université du Québec à Montréal 53, CREFE, Université du Québec à Montréal.
  8. 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, American Statistical Association, vol. 19(3), pages 365-73, July.
  9. João Valle e Azevedo, 2007. "Exact Limit of the Expected Periodogram in the Unit-Root case," Working Papers, Banco de Portugal, Economics and Research Department w200713, Banco de Portugal, Economics and Research Department.
  10. Regina Kaiser & Agustín Maravall, 1999. "Estimation of the business cycle: A modified Hodrick-Prescott filter," Spanish Economic Review, Springer, Springer, vol. 1(2), pages 175-206.
  11. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, Elsevier, vol. 91(2), pages 325-371, August.
  12. 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.
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Cited by:
  1. Andrle, Michal, 2008. "The Role of Trends and Detrending in DSGE Models," MPRA Paper 13289, University Library of Munich, Germany.

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