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Extracting business cycle fluctuations: what do time series filters really do?

  • Arturo Estrella

Various methods are available to extract the "business cycle component" of a given time series variable. These methods may be derived as solutions to frequency extraction or signal extraction problems and differ in both their handling of trends and noise and their assumptions about the ideal time-series properties of a business cycle component. The filters are frequently illustrated by application to white noise, but applications to other processes may have very different and possibly unintended effects. This paper examines several frequently used filters as they apply to a range of dynamic process specifications and derives some guidelines for the use of such techniques.

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Paper provided by Federal Reserve Bank of New York in its series Staff Reports with number 289.

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Date of creation: 2007
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Handle: RePEc:fip:fednsr:289
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  1. Ehlgen, Jurgen, 1998. "Distortionary effects of the optimal Hodrick-Prescott filter," Economics Letters, Elsevier, vol. 61(3), pages 345-349, December.
  2. Lawrence J. Christiano & Terry J. Fitzgerald, 1999. "The Band pass filter," Working Paper 9906, Federal Reserve Bank of Cleveland.
    • 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, 05.
  3. Harvey, A C & Jaeger, A, 1993. "Detrending, Stylized Facts and the Business Cycle," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(3), pages 231-47, July-Sept.
  4. King, R.G. & Rebelo, S.T., 1989. "Low Frequency Filtering And Real Business Cycles," RCER Working Papers 205, University of Rochester - Center for Economic Research (RCER).
  5. Comin, D. & Gertler, M., 2003. "Medium Term Business Cycles," Working Papers 03-05, C.V. Starr Center for Applied Economics, New York University.
  6. Harvey, A.C. & Trimbur, T.M., 2001. "General Model-based Filters for Extracting Cycles and Trends in Economic Time Series," Cambridge Working Papers in Economics 0113, Faculty of Economics, University of Cambridge.
  7. Robert J. Hodrick & Edward Prescott, 1981. "Post-War U.S. Business Cycles: An Empirical Investigation," Discussion Papers 451, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Arturo Estrella, 1997. "A new measure of fit for equations with dichotomous dependent variables," Research Paper 9716, Federal Reserve Bank of New York.
  9. Ulrich K. Müller & Mark W. Watson, 2008. "Testing Models of Low-Frequency Variability," Econometrica, Econometric Society, vol. 76(5), pages 979-1016, 09.
  10. R. F. Engle, 1972. "Band Spectrum Regressions," Working papers 96, Massachusetts Institute of Technology (MIT), Department of Economics.
  11. James G. MacKinnon, 1995. "Numerical Distribution Functions for Unit Root and Cointegration Tests," Working Papers 918, Queen's University, Department of Economics.
  12. Christian J. Murray, 2003. "Cyclical Properties of Baxter-King Filtered Time Series," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 472-476, May.
  13. 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.
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