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A Frequency-selective Filter for Short-Length Time Series

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  • Alain Noullez
  • Alessandra Iacobucci

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 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

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2004 with number 128.

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Date of creation: 11 Aug 2004
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Handle: RePEc:sce:scecf4:128

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Keywords: spectral analysis; bandpass filtering;

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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.
  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. Haldane, Andrew & Quah, Danny, 1999. "UK Phillips Curves and Monetary Policy," CEPR Discussion Papers 2292, C.E.P.R. Discussion Papers.
  4. Ravn, Morten O. & Uhlig, Harald, 2001. "On Adjusting the HP-Filter for the Frequency of Observations," CEPR Discussion Papers 2858, C.E.P.R. Discussion Papers.
  5. 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.
  6. 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.
  7. Andrew Harvey, 2004. "Trend estimation, signal-noise ratios and the frequency of observations," Econometric Society 2004 Australasian Meetings 343, Econometric Society.
  8. 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.
  9. Lawrence J. Christiano & Terry J. Fitzgerald, 1999. "The Band pass filter," Working Paper 9906, Federal Reserve Bank of Cleveland.
    • 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.
  10. 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.
  11. Luca Benati, 2001. "Band-pass filtering, cointegration, and business cycle analysis," Bank of England working papers 142, Bank of England.
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Cited by:
  1. 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.
  2. Jérôme Creel & Francesco Saraceno, 2008. "Automatic Stabilisation, Discretionary Policy and the Stability Pact," Sciences Po publications 2008-15, Sciences Po.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. Robert Dixon & David Shepherd, 2009. "Regional Dimensions of the Australian Business Cycle," Department of Economics - Working Papers Series 1088, The University of Melbourne.
  8. repec:spo:wpecon:info:hdl:2441/6152 is not listed on IDEAS
  9. D.S.G. Pollock, 2008. "Realisations of Finite-Sample Frequency-Selective Filters," Discussion Papers in Economics 08/32, Department of Economics, University of Leicester.
  10. 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).
  11. 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.
  12. 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.
  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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