NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

The Band Pass Filter

Lawrence J. Christiano, Terry J. Fitzgerald

NBER Working Paper No. 7257
Issued in July 1999
NBER Program(s):   EFG

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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Document Object Identifier (DOI): 10.3386/w7257

Published: Christiano, Lawrence J. and Terry J. Fitzgerald. "The Band Pass Filter," International Economic Review, 2003, v44(2,May), 435-465.

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