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 their application to both an artificial, known-structure series and to the Euro zone quarterly GDP series. The Hamming-windowed filter has almost no leakage and is thus much better than the others in eliminating high-frequency components and has a significantly flatter bandpass response. Its low-frequency behavior demonstrates better removal of undesired long-term components. These improvements are particularly evident when working with short-length time series, such as 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