Cyclical Properties of Baxter-King Filtered Time Series

This note demonstrates that the Baxter-King (1999) filter, and in general any bandpass filter, does not isolate the cycle in an unobserved-components model with a stochastic trend. The first difference of the trend passes through the filter, and as a result, the spectral properties of the filtered series depend on the trend in the unfiltered series. It is demonstrated that for postwar U.S. real GDP, the spectral properties of the BK-filtered series are primarily to due to the stochastic trend in output. © 2003 President and Fellows of Harvard College and the Massachusetts Institute of Technology.