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A Frequency Selective Filter for Short-Length Time Series

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  • Alessandra Iacobucci

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  • 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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    Cited by:

    1. 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.
    2. Kufenko, Vadim, 2016. "Spurious periodicities in cliometric series: Simultaneous testing," Violette Reihe: Schriftenreihe des Promotionsschwerpunkts "Globalisierung und Beschäftigung" 48/2016, University of Hohenheim, Carl von Ossietzky University Oldenburg, Evangelisches Studienwerk.
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    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. Christophe Blot & Sabine Le Bayon & Matthieu Lemoine & Sandrine Levasseur, 2009. "De la crise financière à la crise économique. Une analyse comparative France-États-Unis," Revue de l'OFCE, Presses de Sciences-Po, vol. 0(3), pages 255-281.
    6. 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.
    7. Jérôme Creel & Francesco Saraceno, 2008. "Automatic Stabilisation, Discretionary Policy and the Stability Pact," Sciences Po publications 2008-15, Sciences Po.
    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. repec:spo:wpecon:info:hdl:2441/6152 is not listed on IDEAS
    10. D.S.G. Pollock, 2008. "Realisations of Finite-Sample Frequency-Selective Filters," Discussion Papers in Economics 08/32, Department of Economics, University of Leicester.
    11. 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.
    12. Roman Marsalek & Jitka Pomenkova & Svatopluk Kapounek, 2014. "A Wavelet-Based Approach to Filter Out Symmetric Macroeconomic Shocks," Computational Economics, Springer;Society for Computational Economics, vol. 44(4), pages 477-488, December.
    13. Zuzana Kucerova & Jitka Pomenkova, 2014. "Financial and Trade Integration of Selected EU Regions: Dynamic Correlation and Wavelet Approach," MENDELU Working Papers in Business and Economics 2014-45, Mendel University in Brno, Faculty of Business and Economics.
    14. 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).
    15. Mehdi Bhoury & Mohamed Slim Mouha, 2015. "Characteristics of the Tunisian Business Cycle and its International Synchronization," IHEID Working Papers 16-2015, Economics Section, The Graduate Institute of International Studies.
    16. Ashley, Richard & Verbrugge, Randal, 2015. "Persistence Dependence in Empirical Relations: The Velocity of Money," Working Paper 1530, Federal Reserve Bank of Cleveland.
    17. Jitka Poměnková & Svatopluk Kapounek & Roman Maršálek, 2014. "Variability of Dynamic Correlation - The Evidence of Sector-Specific Shocks in V4 Countries," Prague Economic Papers, University of Economics, Prague, vol. 2014(3), pages 371-387.
    18. 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.
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    20. Jitka Poměnková & Roman Maršálek, 2015. "Empirical Evidence of Ideal Filter Approximation: Peripheral and Selected EU Countries Application," Prague Economic Papers, University of Economics, Prague, vol. 2015(5), pages 485-502.
    21. Jovanovic, Branimir, 2007. "Calculating the Fundamental Equilibrium Exchange Rate of the Macedonian Denar," MPRA Paper 43161, University Library of Munich, Germany.
    22. 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.
    23. 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.

    More about this item

    Keywords

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

    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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