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The Band pass filter

Author

Listed:
  • 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, but applying this filter requires a data set of infinite length. In practice, some sort of approximation is needed. Using projections, the authors derive approximations that are optimal when the time-series representations underlying the raw data have a unit root, or are stationary about a trend.

Suggested Citation

  • Lawrence J. Christiano & Terry J. Fitzgerald, 1999. "The Band pass filter," Working Papers (Old Series) 9906, Federal Reserve Bank of Cleveland.
    • Handle: RePEc:fip:fedcwp:9906
    DOI: 10.26509/frbc-wp-199906
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    Other versions of this item:

    • 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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    More about this item

    Keywords

    time series analysis;

    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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