TY  - JOUR
AU  - Christiano,Lawrence J.
AU  - Fitzgerald,Terry J.
TI  - The Band Pass Filter
JF  - National Bureau of Economic Research Working Paper Series
VL  - No. 7257
PY  - 1999
Y2  - July 1999
UR  - http://www.nber.org/papers/w7257
L1  - http://www.nber.org/papers/w7257.pdf
N1  - Author contact info:
Lawrence Christiano
Department of Economics
Northwestern University
2001 Sheridan Road
Evanston, IL 60208
Tel: 847/491-8231
Fax: 847/491-7001
E-Mail: l-christiano@northwestern.edu
AB  - 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.
ER  -