A Frequency Selective Filter for Short-Length Time Series
An effective and easy-to-implement frequency filter is designed by convolving a Hamming window with the ideal rectangular filter response function. Three other filters (Hodrick-Prescott, Baxter-King, and Christiano-Fitzgerald) are critically reviewed. The behavior of the Hamming-windowed filter is compared to the others through their frequency responses and by applying them both to an artificial, known-structure series and the Euro zone GDP quarterly series. As for the Hodrick-Prescott filter, a bandpass version of it is used. The Hamming-windowed filter has almost no leakage and is thus much better than the others at eliminating high frequency components, while the response in the passband is significantly flatter. Moreover, its behavior at low frequencies ensures a better removal of undesired long-term components. Those improvements are particularly evident when working with short-length time series, which are common in Macroeconomics. The proposed filter is stationary, symmetric, uses all the information contained in the raw data and stationarizes series integrated up to order two. It thus proves to be a good candidate for extracting frequency-defined business cycle components.
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