Skip to:
  1. Main navigation
  2. Main content
  3. Footer
Working Paper

The Band Pass Filter

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.

Working Papers of the Federal Reserve Bank of Cleveland are preliminary materials circulated to stimulate discussion and critical comment on research in progress. They may not have been subject to the formal editorial review accorded official Federal Reserve Bank of Cleveland publications. The views expressed in this paper are those of the authors and do not represent the views of the Federal Reserve Bank of Cleveland or the Federal Reserve System.


Suggested Citation

Christiano, Lawrence, and Terry J. Fitzgerald. 1999. “The Band Pass Filter.” Federal Reserve Bank of Cleveland, Working Paper No. 99-06. https://doi.org/10.26509/frbc-wp-199906