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The Band Pass Filter

  • Lawrence J. Christiano
  • Terry J. Fitzgerald

We develop optimal finite-sample approximations for the band pass filter. These approximations include one-sided filters that can be used in real time. Optimal approximations depend upon the details of the time series representation that generates the data. Fortunately, for U.S. macroeconomic data, getting the details exactly right is not crucial. A simple approach, based on the generally false assumption that the data are generated by a random walk, is nearly optimal. We use the tools discussed here to document a new fact: There has been a significant shift in the money-inflation relationship before and after 1960. Copyright 2003 By The Economics Department Of The University Of Pennsylvania And Osaka University Institute Of Social And Economic Research Association.

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Article provided by Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association in its journal International Economic Review.

Volume (Year): 44 (2003)
Issue (Month): 2 (05)
Pages: 435-465

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Handle: RePEc:ier:iecrev:v:44:y:2003:i:2:p:435-465
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