IDEAS home Printed from https://ideas.repec.org/p/fce/doctra/0405.html
   My bibliography  Save this paper

A Frequency Selective Filter for Short-Length Time Series

Author

Listed:

Abstract

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.

Suggested Citation

  • Alessandra Iacobucci & Alain Noullez, 2004. "A Frequency Selective Filter for Short-Length Time Series," Documents de Travail de l'OFCE 2004-05, Observatoire Francais des Conjonctures Economiques (OFCE).
    • Handle: RePEc:fce:doctra:0405
    as

    Download full text from publisher

    File URL: http://www.ofce.sciences-po.fr/pdf/dtravail/WP2004-05.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Marianne Baxter & Robert G. King, 1999. "Measuring Business Cycles: Approximate Band-Pass Filters For Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 575-593, November.
    2. 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.
    3. Uhlig, H.F.H.V.S. & Ravn, M., 1997. "On Adjusting the H-P Filter for the Frequency of Observations," Discussion Paper 1997-50, Tilburg University, Center for Economic Research.
    4. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
    5. Andrew C. Harvey & Thomas M. Trimbur, 2003. "General Model-Based Filters for Extracting Cycles and Trends in Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 244-255, May.
    6. Arthur F. Burns & Wesley C. Mitchell, 1946. "Measuring Business Cycles," NBER Books, National Bureau of Economic Research, Inc, number burn46-1.
    7. Lawrence J. Christiano & Terry J. Fitzgerald, 2003. "The Band Pass Filter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(2), pages 435-465, May.
    8. Luca Benati, 2001. "Band-pass filtering, cointegration, and business cycle analysis," Bank of England working papers 142, Bank of England.
    9. Haldane, Andrew & Quah, Danny, 1999. "UK Phillips curves and monetary policy," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 259-278, October.
    10. Andrew Harvey, 2004. "Trend estimation, signal-noise ratios and the frequency of observations," Econometric Society 2004 Australasian Meetings 343, Econometric Society.
    11. Stock, James H. & Watson, Mark W., 1999. "Business cycle fluctuations in us macroeconomic time series," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 1, pages 3-64, Elsevier.
    12. Gomez, Victor, 2001. "The Use of Butterworth Filters for Trend and Cycle Estimation in Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(3), pages 365-373, July.
    13. King, Robert G. & Rebelo, Sergio T., 1993. "Low frequency filtering and real business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 17(1-2), pages 207-231.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Álvarez, Luis J. & Gómez-Loscos, Ana, 2018. "A menu on output gap estimation methods," Journal of Policy Modeling, Elsevier, vol. 40(4), pages 827-850.
    2. Ard den Reijer, 2006. "The Dutch business cycle: which indicators should we monitor?," DNB Working Papers 100, Netherlands Central Bank, Research Department.
    3. Lechman, Ewa & Dominiak, Piotr, 2016. "Entrepreneurship vulnerability to business cycle. A new methodology for identification pro-cyclical and counter-cyclical patterns of entrepreneurial activity," MPRA Paper 68793, University Library of Munich, Germany.
    4. Arturo Estrella, 2007. "Extracting business cycle fluctuations: what do time series filters really do?," Staff Reports 289, Federal Reserve Bank of New York.
    5. Dilip Nachane & Aditi Chaubal, 2022. "A Comparative Evaluation of Some DSP Filters vis-à-vis Commonly Used Economic Filters," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 161-190, September.
    6. Galimberti, Jaqueson K. & Moura, Marcelo L., 2016. "Improving the reliability of real-time output gap estimates using survey forecasts," International Journal of Forecasting, Elsevier, vol. 32(2), pages 358-373.
    7. Hall, Viv B & Thomson, Peter, 2022. "A boosted HP filter for business cycle analysis: evidence from New Zealand’s small open economy," Working Paper Series 9473, Victoria University of Wellington, School of Economics and Finance.
    8. Luca Benati, 2001. "Band-pass filtering, cointegration, and business cycle analysis," Bank of England working papers 142, Bank of England.
    9. Viv B. Hall & Peter Thomson, 2021. "Does Hamilton’s OLS Regression Provide a “better alternative” to the Hodrick-Prescott Filter? A New Zealand Business Cycle Perspective," Journal of Business Cycle Research, Springer;Centre for International Research on Economic Tendency Surveys (CIRET), vol. 17(2), pages 151-183, November.
    10. Aadland, David, 2005. "Detrending time-aggregated data," Economics Letters, Elsevier, vol. 89(3), pages 287-293, December.
    11. Thomas M. Trimbur, 2006. "Detrending economic time series: a Bayesian generalization of the Hodrick-Prescott filter," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(4), pages 247-273.
    12. Robert J. Hodrick, 2020. "An Exploration of Trend-Cycle Decomposition Methodologies in Simulated Data," NBER Working Papers 26750, National Bureau of Economic Research, Inc.
    13. João Valle e Azevedo, 2007. "A Multivariate Band-Pass Filter," Working Papers w200717, Banco de Portugal, Economics and Research Department.
    14. Andrew C. Harvey & Thomas M. Trimbur, 2003. "General Model-Based Filters for Extracting Cycles and Trends in Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 244-255, May.
    15. Strohsal, Till & Proaño, Christian R. & Wolters, Jürgen, 2019. "Characterizing the financial cycle: Evidence from a frequency domain analysis," Journal of Banking & Finance, Elsevier, vol. 106(C), pages 568-591.
    16. Michael Funke & Harm Bandholz, 2003. "In search of leading indicators of economic activity in Germany," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 22(4), pages 277-297.
    17. João Valle e Azevedo, 2007. "Interpretation of the Effects of Filtering Integrated Time Series," Working Papers w200712, Banco de Portugal, Economics and Research Department.
    18. de Carvalho, Miguel & Rua, António, 2017. "Real-time nowcasting the US output gap: Singular spectrum analysis at work," International Journal of Forecasting, Elsevier, vol. 33(1), pages 185-198.
    19. Ángel Guillén & Gabriel Rodríguez, 2014. "Trend-cycle decomposition for Peruvian GDP: application of an alternative method," Latin American Economic Review, Springer;Centro de Investigaciòn y Docencia Económica (CIDE), vol. 23(1), pages 1-44, December.
    20. Viv B. Hall & Peter Thomson, 2022. "A boosted HP filter for business cycle analysis:evidence from New Zealand's small open economy," CAMA Working Papers 2022-45, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.

    More about this item

    Keywords

    Spectral methods; frequency selective filters; Hodrick-Prescott; 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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:fce:doctra:0405. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Francesco Saraceno (email available below). General contact details of provider: https://edirc.repec.org/data/ofcspfr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.