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The Band Pass Filter

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  • Lawrence J. Christiano
  • Terry J. Fitzgerald

Abstract

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.

Suggested Citation

  • Lawrence J. Christiano & Terry J. Fitzgerald, 1999. "The Band Pass Filter," NBER Working Papers 7257, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:7257
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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, May.

    References listed on IDEAS

    as
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    JEL classification:

    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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