The `ideal' band pass filter can be used to isolate the component of a time series that lies within a particular band of frequencies. However, applying this filter requires a dataset of infinite length. In practice, some sort of approximation is needed. Using projections, we derive approximations that are optimal when the time series representations underlying the raw data have a unit root, or are stationary about a trend. We identify one approximation which, though it is only optimal for one particular time series representation, nevertheless works well for standard macroeconomic time series. To illustrate the use of this approximation, we use it to characterize the change in the nature of the Phillips curve and the money-inflation relation before and after the 1960s. We find that there is surprisingly little change in the Phillips curve and substantial change in money growth-inflation relation.
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number
7257.
Length: Date of creation: Jul 1999 Date of revision: Handle: RePEc:nbr:nberwo:7257
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Article
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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Paper
Lawrence J. Christiano & Terry J. Fitzgerald, 1999.
"The Band pass filter,"
Working Paper
9906, Federal Reserve Bank of Cleveland.
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Find related papers by JEL classification: E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General
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Laurence Ball & N. Gregory Mankiw, 1995.
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Engle, Robert F, 1974.
"Band Spectrum Regression,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 1-11, February.
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