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A Frequency Selective Filter for Short-Length Time Series

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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.

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Paper provided by Observatoire Francais des Conjonctures Economiques (OFCE) in its series Documents de Travail de l'OFCE with number 2004-05.

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Date of creation: 2004
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Handle: RePEc:fce:doctra:0405

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Keywords: Spectral methods; frequency selective filters; Hodrick-Prescott; Baxter-King and Christiano-Fitzgerald bandpass filters; business cycles.;

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  1. Robert J. Hodrick & Edward Prescott, 1981. "Post-War U.S. Business Cycles: An Empirical Investigation," Discussion Papers 451, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. 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.
  3. Andrew Harvey, 2004. "Trend estimation, signal-noise ratios and the frequency of observations," Econometric Society 2004 Australasian Meetings 343, Econometric Society.
  4. 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.
  5. Morten O. Ravn & Harald Uhlig, 2001. "On Adjusting the HP-Filter for the Frequency of Observations," CESifo Working Paper Series 479, CESifo Group Munich.
  6. Andrew Haldane & Danny Quah, 2000. "UK Philips Curves and Monetary Policy," CEP Discussion Papers dp0444, Centre for Economic Performance, LSE.
  7. King, R.G. & Rebelo, S.T., 1989. "Low Frequency Filtering And Real Business Cycles," RCER Working Papers 205, University of Rochester - Center for Economic Research (RCER).
  8. 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.
  9. 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.
  10. Luca Benati, 2001. "Band-pass filtering, cointegration, and business cycle analysis," Bank of England working papers 142, Bank of England.
  11. 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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Citations

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Cited by:
  1. 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.
  2. Robert Dixon & David Shepherd, 2009. "Regional Dimensions of the Australian Business Cycle," Department of Economics - Working Papers Series 1088, The University of Melbourne.
  3. 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.
  4. 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.
  5. 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.
  6. repec:spo:wpecon:info:hdl:2441/6152 is not listed on IDEAS
  7. 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).
  8. D.S.G. Pollock, 2008. "Realisations of Finite-Sample Frequency-Selective Filters," Discussion Papers in Economics 08/32, Department of Economics, University of Leicester.
  9. 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.
  10. 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.
  11. 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.
  12. Jérôme Creel & Francesco Saraceno, 2008. "Automatic Stabilisation, Discretionary Policy and the Stability Pact," Sciences Po publications 2008-15, Sciences Po.
  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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