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

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Author Info
Harvey, A.C.
Trimbur, T.M.

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Abstract

A new class of model-based filters for extracting trends and cycles in economic time series is presented. These low pass and band pass 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 a Kalman filter and associated smoother. The filters form a class which is a generalisation 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, band pass filters emerge as a special case. Applying the method to a quarterly series on US investment shows a clearly defined cycle currently at the peak of a boom.

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File URL: http://www.econ.cam.ac.uk/dae/repec/cam/pdf/wp0113.pdf
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Publisher Info
Paper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 0113.

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Length: 21
Date of creation: Jul 2001
Date of revision:
Handle: RePEc:cam:camdae:0113

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Related research
Keywords: band pass filter; Butterworth filter; ideal filter; Kalman filter; signal extraction; unobserved components;

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Find related papers by JEL classification:
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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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.:
  1. Marianne Baxter & Robert G. King, 1999. "Measuring Business Cycles: Approximate Band-Pass Filters For Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 575-593, November. [Downloadable!] (restricted)
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  2. Lawrence J. Christiano & Terry J. Fitzgerald, 1999. "The Band Pass Filter," NBER Working Papers 7257, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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    • Lawrence J. Christiano & Terry J. Fitzgerald, 1999. "The Band pass filter," Working Paper 9906, Federal Reserve Bank of Cleveland. [Downloadable!]
    • 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)
  3. Luca Benati, . "Band-pass filtering, cointegration, and business cycle analysis," Bank of England working papers 142, Bank of England. [Downloadable!]
  4. 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. [Downloadable!] (restricted)
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  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. [Downloadable!]
    Other versions:
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This page was last updated on 2009-11-16.

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