24 Pages Posted: 7 Mar 2017
Date Written: January 1, 2006
In the following article the ideal band-pass filter is derived and explained in order to subsequently analyze the approximations by Baxter and King (1999) and Christiano and Fitzgerald (2003). It can be shown that the filters by Baxter and King and Christiano and Fitzgerald primarily differ in two assumptions, namely in the assumption about the spectral density of the analyzed variables as well as in the assumption about the symmetry of the weights of the band-pass filter. In the article at hand it is shown that the different assumptions lead to characteristics for the two filters which distinguish in three points: in the accuracy of the approximation with respect to the length of the cycles considered, in theamount of calculable data points towards the ends of the data series, as well as in the removal of the trend of the original time series.
Keywords: Business Cycles, Band-Pass Filter, Spectral Density
JEL Classification: E32, E37
Suggested Citation: Suggested Citation