02081cam a22002657 4500001000600000003000500006005001700011008004100028100002800069245009600097260006600193490004100259500001500300520091500315530006101230538007201291538003601363690009001399690011001489700002501599710004201624830007601666856003701742856003601779w7257NBER20150525182027.0150525s1999 mau||||fs|||| 000 0 eng d1 aChristiano, Lawrence J.14aThe Band Pass Filterh[electronic resource] /cLawrence J. Christiano, Terry J. Fitzgerald. aCambridge, Mass.bNational Bureau of Economic Researchc1999.1 aNBER working paper seriesvno. w7257 aJuly 1999.3 aThe `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. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web. 7aE3 - Prices, Business Fluctuations, and Cycles2Journal of Economic Literature class. 7aC1 - Econometric and Statistical Methods and Methodology: General2Journal of Economic Literature class.1 aFitzgerald, Terry J.2 aNational Bureau of Economic Research. 0aWorking Paper Series (National Bureau of Economic Research)vno. w7257.4 uhttp://www.nber.org/papers/w725741uhttp://dx.doi.org/10.3386/w7257