An Investigation of the Cycle Extraction Properties of Several Bandpass Filters Used to Identify Business Cycles
The purpose of this article is to investigate the ability of bandpass filters commonly used in economics to extract a known periodicity. The specific bandpass filters investigated include a Discrete Fourier Transform (DFT) filter, together with those proposed by Hodrick and Prescott (1997) and Baxter and King (1999). Our focus on the cycle extraction properties of these filters reflects the lack of attention that has been given to this issue in the literature, when compared, for example, to studies of the trend removal properties of some of these filters. The artificial data series we use are designed so that one periodicity deliberately falls within the passband while another falls outside. The objective of a filter is to admit the ‘bandpass’ periodicity while excluding the periodicity that falls outside the passband range. We find that the DFT filter has the best extraction properties. The filtered data series produced by both the Hodrick-Prescott and Baxter-King filters are found to admit low frequency components that should have been excluded.
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- Robert J. Hodrick & Edward Prescott, 1981.
"Post-War U.S. Business Cycles: An Empirical Investigation,"
451, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
- King, Robert G. & Rebelo, Sergio T., 1993.
"Low frequency filtering and real business cycles,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 17(1-2), pages 207-231.
- 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.
- Marianne Baxter & Robert G. King, 1995. "Measuring Business Cycles Approximate Band-Pass Filters for Economic Time Series," NBER Working Papers 5022, National Bureau of Economic Research, Inc.
- Tom Doan, . "BKFILTER: RATS procedure to implement band pass filter using Baxter-King method," Statistical Software Components RTS00026, Boston College Department of Economics.
- Timothy Cogley & James M. Nason, 1993.
"Effects of the Hodrick-Prescott filter on trend and difference stationary time series: implications for business cycle research,"
Working Papers in Applied Economic Theory
93-01, Federal Reserve Bank of San Francisco.
- Cogley, Timothy & Nason, James M., 1995. "Effects of the Hodrick-Prescott filter on trend and difference stationary time series Implications for business cycle research," Journal of Economic Dynamics and Control, Elsevier, vol. 19(1-2), pages 253-278.
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