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A Frequency Selective Filter for Short-Length Time Series

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Date
2005
Dewey
Probabilités et mathématiques appliquées
Sujet
business cycles; spectral methods; Baxter–King and Christiano–Fitzgerald bandpass filters; frequency domain filtering; HP filter
JEL code
C10; C14; E32
Journal issue
Computational Economics
Volume
25
Number
1-2
Publication date
2005
Article pages
75-1002
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s10614-005-6276-7
URI
https://basepub.dauphine.fr/handle/123456789/10488
Collections
  • CEREMADE : Publications
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Author
Iacobucci, Alessandra
Noullez, Alain
Type
Article accepté pour publication ou publié
Abstract (EN)
An effective and easy-to-implement frequency filter is proposed, obtained by convolving a raised-cosine window with the ideal rectangular filter response function. Three other filters, Hodrick–Prescott, Baxter–King, and Christiano–Fitzgerald, are thoroughly reviewed. A bandpass version of the Hodrick–Prescott filter is also introduced and used. The behavior of the windowed filter is compared to the others through their frequency responses and by applying them to both quarterly and monthly artificial, known-structure series and real macroeconomic data. The windowed filter has almost no leakage and is better than the others at eliminating high-frequency components. Its response in the passband is significantly flatter, and its behavior at low frequencies ensures a better removal of undesired long-term components. These improvements are particularly evident when working with short-length time series, which are common in macroeconomics. The proposed filter is stationary and symmetric, therefore, it induces no phase-shift. It uses all the information contained in the input data and stationarizes series integrated up to order two. It thus proves to be a good candidate for extracting frequency-defined series components.

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