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A Frequency Selective Filter for Short-Length Time Series

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  • Alessandra Iacobucci
  • Alain Noullez

Abstract

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. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • Alessandra Iacobucci & Alain Noullez, 2005. "A Frequency Selective Filter for Short-Length Time Series," Computational Economics, Springer;Society for Computational Economics, vol. 25(1), pages 75-102, February.
    • Handle: RePEc:kap:compec:v:25:y:2005:i:1:p:75-102
    DOI: 10.1007/s10614-005-6276-7
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    References listed on IDEAS

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    1. Christian J. Murray, 2003. "Cyclical Properties of Baxter-King Filtered Time Series," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 472-476, May.
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    More about this item

    Keywords

    frequency domain filtering; spectral methods; HP filter; Baxter–King and Christiano–Fitzgerald bandpass filters; business cycles;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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