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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

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File URL: http://hdl.handle.net/10.1007/s10614-005-6276-7
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Bibliographic Info

Article provided by Society for Computational Economics in its journal Computational Economics.

Volume (Year): 25 (2005)
Issue (Month): 1 (February)
Pages: 75-102

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Handle: RePEc:kap:compec:v:25:y:2005:i:1:p:75-102

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Web page: http://www.springerlink.com/link.asp?id=100248
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Related research

Keywords: frequency domain filtering; spectral methods; HP filter; Baxter–King and Christiano–Fitzgerald bandpass filters; business cycles;

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References

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  1. Haldane, Andrew & Quah, Danny, 1999. "UK Phillips curves and monetary policy," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 259-278, October.
  2. 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.
  3. 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.
  4. Andrew Harvey, 2004. "Trend estimation, signal-noise ratios and the frequency of observations," Econometric Society 2004 Australasian Meetings 343, Econometric Society.
  5. 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.
  6. 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, 05.
  7. Harvey, A.C. & Trimbur, T.M., 2001. "General Model-based Filters for Extracting Cycles and Trends in Economic Time Series," Cambridge Working Papers in Economics 0113, Faculty of Economics, University of Cambridge.
  8. 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.
  9. 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 365-73, July.
  10. Luca Benati, 2001. "Band-pass filtering, cointegration, and business cycle analysis," Bank of England working papers 142, Bank of England.
  11. James H. Stock & Mark W. Watson, 1998. "Business Cycle Fluctuations in U.S. Macroeconomic Time Series," NBER Working Papers 6528, National Bureau of Economic Research, Inc.
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Cited by:
  1. David Shepherd & Robert Dixon, 2010. "The not-so-great moderation? Evidence on changing volatility from Australian regions," Department of Economics - Working Papers Series 1090, The University of Melbourne.
  2. Ghate, Chetan & Pandey, Radhika & Patnaik, Ila, 2013. "Has India emerged? Business cycle stylized facts from a transitioning economy," Structural Change and Economic Dynamics, Elsevier, vol. 24(C), pages 157-172.
  3. Ghate, Chetan & Pandey, Radhika & Patnaik, Ila, 2011. "Has India emerged? Business cycle facts from a transitioning economy," Working Papers 11/88, National Institute of Public Finance and Policy.
  4. Robert Dixon & David Shepherd, 2013. "Regional Dimensions of the Australian Business Cycle," Regional Studies, Taylor & Francis Journals, vol. 47(2), pages 264-281, February.
  5. D.S.G. Pollock, 2008. "Realisations of Finite-Sample Frequency-Selective Filters," Discussion Papers in Economics 08/32, Department of Economics, University of Leicester.
  6. repec:spo:wpecon:info:hdl:2441/6152 is not listed on IDEAS
  7. Matteo Pelagatti & Valeria Negri, 2008. "Milan’s Cycle as an Accurate Leading Indicator for the Italian Business Cycle," Working Papers 20080601, Università degli Studi di Milano-Bicocca, Dipartimento di Statistica.
  8. Prof D.S.G. Pollock, 2008. "The Realisation of Finite-Sample Frequency-Selective Filters," Discussion Papers in Economics 08/13, Department of Economics, University of Leicester.
  9. Matthieu Lemoine, 2005. "A model of the stochastic convergence between business cycles," Documents de Travail de l'OFCE 2005-05, Observatoire Francais des Conjonctures Economiques (OFCE).
  10. Jerome Creel & Francesco Saraceno, 2008. "Automatic Stabilisation, Discretionary Policy and the Stability Pact," Documents de Travail de l'OFCE 2008-15, Observatoire Francais des Conjonctures Economiques (OFCE).
  11. Schoch, Tobias & Staub, Kaspar & Pfister, Christian, 2012. "Social inequality and the biological standard of living: An anthropometric analysis of Swiss conscription data, 1875–1950," Economics & Human Biology, Elsevier, vol. 10(2), pages 154-173.
  12. Svatopluk Kapounek & Jitka Pomenkova, 2012. "Spurious synchronization of business cycles: Dynamic correlation analysis of V4 countries," MENDELU Working Papers in Business and Economics 2012-22, Mendel University in Brno, Faculty of Business and Economics.
  13. Jovanovic, Branimir, 2007. "Calculating the Fundamental Equilibrium Exchange Rate of the Macedonian Denar," MPRA Paper 43161, University Library of Munich, Germany.

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