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. Copyright (c) 2003 President and Fellows of Harvard College and the Massachusetts Institute of Technology.
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Lawrence J. Christiano & Terry J. Fitzgerald, 1999.
"The Band Pass Filter,"
NBER Working Papers
7257, National Bureau of Economic Research, Inc.
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Lawrence J. Christiano & Terry J. Fitzgerald, 1999.
"The Band pass filter,"
Working Paper
9906, Federal Reserve Bank of Cleveland.
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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.
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