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L'approximation du filtre passe-bande proposée par Christiano et Fitzgerald

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  • Jean-Yves Fournier

    (INSEE - Institut national de la statistique et des études économiques (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

  • Jean-Yves Fournier, 2000. "L'approximation du filtre passe-bande proposée par Christiano et Fitzgerald," Working Papers hal-05358436, HAL.
    • Handle: RePEc:hal:wpaper:hal-05358436
    Note: View the original document on HAL open archive server: https://insee.hal.science/hal-05358436v1
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