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Interpretation of the Effects of Filtering Integrated Time Series

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Author Info
Valle e Azevedo, João

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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 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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Related research
Keywords: Unit roots Band-pass filters Pseudo-spectrum

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Find related papers by JEL classification:
E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models

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  1. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August. [Downloadable!] (restricted)
  2. Canova, Fabio, 1998. "Detrending and business cycle facts," Journal of Monetary Economics, Elsevier, vol. 41(3), pages 475-512, May. [Downloadable!] (restricted)
    Other versions:
  3. King, Robert G. & Rebelo, Sergio T., 1993. "Low frequency filtering and real business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 17(1-2), pages 207-231. [Downloadable!] (restricted)
    Other versions:
  4. Lawrence J. Christiano & Terry J. Fitzgerald, 1999. "The Band pass filter," Working Paper 9906, Federal Reserve Bank of Cleveland. [Downloadable!]
    Other versions:
    • Lawrence J. Christiano & Terry J. Fitzgerald, 1999. "The Band Pass Filter," NBER Working Papers 7257, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    • 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. [Downloadable!] (restricted)
  5. Andrés Bujosa & Marcos Bujosa & Antonio García Ferrer, 2002. "A Note on the Pseudo-Spectra and the Pseudo-Covariance Generating Functions of ARMA Processes," Documentos del Instituto Complutense de Análisis Económico 0203, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales. [Downloadable!]
  6. Valle e Azevedo, João, 2007. "Exact Limit of the Expected Periodogram in the Unit-Root Case," MPRA Paper 6553, University Library of Munich, Germany. [Downloadable!]
  7. 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, 03. [Downloadable!] (restricted)
  8. Adrian Pagan, 1999. "The Getting of Macroeconomic Wisdom," CEPR Discussion Papers 412, Centre for Economic Policy Research, Research School of Social Sciences, Australian National University. [Downloadable!]
  9. 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.
  10. 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 53, CREFE, Université du Québec à Montréal. [Downloadable!]
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