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Band-Pass Filters

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  • Everts, Martin

Abstract

In the following article the ideal band-pass filter is derived and explained in order to subsequently analyze the approximations by Baxter and King (1999) and Christiano and Fitzgerald (2003). It can be shown that the filters by Baxter and King and Christiano and Fitzgerald primarily differ in two assumptions, namely in the assumption about the spectral density of the analyzed variables as well as in the assumption about the symmetry of the weights of the band-pass filter. In the article at hand it is shown that the different assumptions lead to characteristics for the two filters which distinguish in three points: in the accuracy of the approximation with respect to the length of the cycles considered, in the amount of calculable data points towards the ends of the data series, as well as in the removal of the trend of the original time series.

Suggested Citation

  • Everts, Martin, 2006. "Band-Pass Filters," MPRA Paper 2049, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:2049
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    File URL: https://mpra.ub.uni-muenchen.de/2049/1/MPRA_paper_2049.pdf
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. Sean J. Gossel & Nicholas Biekpe, 2013. "The Cyclical Relationships Between South Africa's Net Capital Inflows and Fiscal and Monetary Policies," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 49(2), pages 64-83, March.
    2. Everts, Martin, 2006. "Duration of Business Cycles," MPRA Paper 1219, University Library of Munich, Germany.
    3. Marco Gallegati & Mauro Gallegati & James B. Ramsey & Willi Semmler, 2017. "Long waves in prices: new evidence from wavelet analysis," Cliometrica, Springer;Cliometric Society (Association Francaise de Cliométrie), vol. 11(1), pages 127-151, January.
    4. Gallegati, Marco & Delli Gatti, Domenico, 2018. "Macrofinancial imbalances in historical perspective: A global crisis index," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 190-205.

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    More about this item

    Keywords

    Business Cycle; Band-Pass Filter;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles

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