Band-Pass Filters

Everts, Martin (2006): Band-Pass Filters. Unpublished.

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.

• Item Type: MPRA Paper
• Institution: University of Bern
• Language: English
• Keywords: Business Cycle; Band-Pass Filter
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles

References

Baxter, M., and R. G. King (1999): “Measuring Business Cycles: Approximate Band-Pass Filters For Economic Time Series,” The Review of Economics and Statistics, 81(4), 575–593. Christiano, L. J., and T. J. Fitzgerald (2003): “The Band Pass Filter,” International Economic Review, 44(2), 435–65. de Moivre, A. (1722): “De Fractionibus Algebraicis Radicalitate Immunibus ad Fractiones Simpliciores Reducendis, Deque Summandis Terminis Quarumdam Serierum Aequali Intervallo a Se Distantibus,” Philosophical Transactions, 32, 162–178. Euler, L. (1793): “Observationes generales circa series, quarum termini secundum sinus vel cosinus angulorum multiplorum progrediuntur,” in Nova Acta Academiae Scientiarum Imperialis Petropolitanae, chap. 7, pp. 87–98. St. Petersburg Academy Publications. Fourier, J. B. J. (1822): Th´eorie analytique de la chaleur. Firmin Didot, P`ere et fils, Paris. Koopmans, L. (1974): The Spectral Analysis of Time Series. Academic Press, New York. 24