Cyclical Properties of Baxter-King Filtered Time Series

By C. Murray. Review of Economics and Statistics, 2003

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The Asymmetric Business Cycle (2012, background): “…operator) is used up transforming the series to something that could be thought of as stationary, leaving the rest of the filter to amplify fluctuations in the transformed series at different frequencies than originally intended (see Cogley & Nason, 1995, and Murray, 2003, on this point).”
Business, Housing and Credit Cycles (2018, background): “Non-parametric filters rely on pre-specified frequency bands, which implies a risk of missing parts of cyclical dynamics or, conversely, of obtaining spurious cycles (Murray, 2003).”
Spectral Analysis for Economic Time Series (2005, background): “[3, 19]) — typically to separate the business cycle from the trend in a model where the latter is nonstationary, e.”
A Frequency Selective Filter for Short-Length Time Series (2005, background): “Finally, for the seek of completeness, we deem it advisable to mention the main limit of these nonparametric filtering procedures, that is, their inability to extract the cycle component if the series is known to have an integrated trend (Benati (2001); Murray (2003)).”