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The approximate band-pass filter proposed by Christiano and Fitzgerald

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  • J.-Y. FOURNIER

    (Insee)

Abstract

Detrending time series and isolating cyclical fluctuations is crucial for business cycle analysis and definition of economic policy. Band-pass filters provide a set of statistical methods to extract the cycle, defined according to a specified range of periodicities. Christiano and Fitzgerald recently proposed a finite approximate band-pass filter, optimal for each time series. In this paper, we present the construction of this optimal approximation under the assumption that the data is generated by a pure random walk. Then, the approximate filter has good properties. It is close to the ideal filter. We illustrate this study by applying the filter to the logarithm of french GDP, and we compare this business cycle to the cycles issued of alternative methods.

Suggested Citation

  • J.-Y. Fournier, 2000. "The approximate band-pass filter proposed by Christiano and Fitzgerald," Documents de Travail de l'Insee - INSEE Working Papers g2000-03, Institut National de la Statistique et des Etudes Economiques.
    • Handle: RePEc:nse:doctra:g2000-03
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    File URL: https://www.bnsp.insee.fr/ark:/12148/bc6p06zqr1f/f1.pdf
    File Function: Document de travail de la DESE numéro G2000-03
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    More about this item

    Keywords

    business cycle; linear filter;

    JEL classification:

    • E30 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - General (includes Measurement and Data)
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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