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General Model-Based Filters for Extracting Cycles and Trends in Economic Time Series

  • Andrew C. Harvey

    (Faculty of Economics and Politics, Cambridge University)

  • Thomas M. Trimbur

    (Faculty of Economics and Politics, Cambridge University)

A class of model-based filters for extracting trends and cycles in economic time series is presented. These lowpass and bandpass filters are derived in a mutually consistent manner as the joint solution to a signal extraction problem in an unobserved-components model. The resulting trends and cycles are computed in finite samples using the Kalman filter and associated smoother. The filters form a class which is a generalization of the class of Butterworth filters, widely used in engineering. They are very flexible and have the important property of allowing relatively smooth cycles to be extracted from economic time series. Perfectly sharp, or ideal, bandpass filters emerge as a limiting case. Applying the method to quarterly series on U.S. investment and GDP shows a clearly defined cycle. © 2003 President and Fellows of Harvard College and the Massachusetts Institute of Technology.

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Article provided by MIT Press in its journal Review of Economics and Statistics.

Volume (Year): 85 (2003)
Issue (Month): 2 (May)
Pages: 244-255

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Handle: RePEc:tpr:restat:v:85:y:2003:i:2:p:244-255
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  1. 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.
  2. 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.
  3. 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.
  4. Luca Benati, 2001. "Band-pass filtering, cointegration, and business cycle analysis," Bank of England working papers 142, Bank of England.
  5. 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.
  6. Koopman, Siem Jan & Harvey, Andrew, 2003. "Computing observation weights for signal extraction and filtering," Journal of Economic Dynamics and Control, Elsevier, vol. 27(7), pages 1317-1333, May.
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