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Identifying the Cycle of a Macroeconomic Time-Series Using Fuzzy Filtering

This paper presents a new method for extracting the cycle from an economic time series. This method uses the fuzzy c-means clustering algorithm, drawn from the pattern recognition literature, to identify groups of observations. The time series is modeled over each of these sub-samples, and the results are combined using the “degrees of membership” for each data-point with each cluster. The result is a totally flexible model that readily captures complex non-linearities in the data. This type of “fuzzy regression” analysis has been shown by Giles and Draeseke (2003) to be highly effective in a broad range of situations with economic data. The fuzzy filter that we develop here is compared with the well-known Hodrick-Prescott (HP) filter in a Monte Carlo experiment, and the new filter is found to perform as well as, or better than, the HP filter. The advantage of the fuzzy filter is especially pronounced when the data have a deterministic, rather than stochastic, trend. Applications with real time-series illustrate the different conclusions that can emerge when the fuzzy regression filter and the HP filter are each applied to extract the cycle.

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Paper provided by Department of Economics, University of Victoria in its series Econometrics Working Papers with number 0406.

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Length: 24 pages
Date of creation: 29 Dec 2004
Date of revision:
Handle: RePEc:vic:vicewp:0406
Note: ISSN 1485-6441
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  1. Sichel, Daniel E, 1989. "Are Business Cycles Asymmetric? A Correction," Journal of Political Economy, University of Chicago Press, vol. 97(5), pages 1255-60, October.
  2. Canova, Fabio, 1993. "Detrending and Business Cycle Facts," CEPR Discussion Papers 782, C.E.P.R. Discussion Papers.
  3. Alain GUAY & Pierre SAINT-AMANT, 2005. "Do the Hodrick-Prescott and Baxter-King Filters Provide a Good Approximation of Business Cycles?," Annales d'Economie et de Statistique, ENSAE, issue 77, pages 133-155.
  4. 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.
  5. Daniel Levy & Hashem Dezhbakhsh, 2002. "On the Typical Spectral Shape of an Economic Variable," Working Papers 2002-16, Bar-Ilan University, Department of Economics.
  6. David E. A. Giles & Robert Draeseke, 2001. "Econometric Modelling based on Pattern recognition via the Fuzzy c-Means Clustering Algorithm," Econometrics Working Papers 0101, Department of Economics, University of Victoria.
  7. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July.
  8. Schlicht, Ekkehart, 2004. "Estimating the Smoothing Parameter in the So-Called Hodrick-Prescott Filter," Discussion Papers in Economics 304, University of Munich, Department of Economics.
  9. Claude Giorno & Pete Richardson & Deborah Roseveare & Paul van den Noord, 1995. "Estimating Potential Output, Output Gaps and Structural Budget Balances," OECD Economics Department Working Papers 152, OECD Publishing.
  10. Randal Verbrugge Randal Verbrugge, 1997. "Investigating Cyclical Asymmetries," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 2(1), pages 1-10, April.
  11. Andrew Rennison, 2003. "Comparing Alternative Output-Gap Estimators: A Monte Carlo Approach," Working Papers 03-8, Bank of Canada.
  12. Jane Haltmaier, 2001. "The use of cyclical indicators in estimating the output gap in Japan," International Finance Discussion Papers 701, Board of Governors of the Federal Reserve System (U.S.).
  13. 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.
  14. 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.
  15. Giles, David E A, 1997. "Testing for Asymmetry in the Measured and Underground Business Cycles in New Zealand," The Economic Record, The Economic Society of Australia, vol. 73(222), pages 225-32, September.
  16. W.A. Razzak, 2001. "Business Cycle Asymmetries: International Evidence," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 4(1), pages 230-243, January.
  17. Neftci, Salih N, 1984. "Are Economic Time Series Asymmetric over the Business Cycle?," Journal of Political Economy, University of Chicago Press, vol. 92(2), pages 307-28, April.
  18. Martin Sola & Zacharias Psaradakis, 2002. "On Detrending and Cyclical Asymmetry," Department of Economics Working Papers 020, Universidad Torcuato Di Tella.
  19. 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.
  20. Alasdair Scott, 2000. "Stylised facts from output gap measures," Reserve Bank of New Zealand Discussion Paper Series DP2000/07, Reserve Bank of New Zealand.
  21. 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.
  22. repec:dgr:kubcen:199750 is not listed on IDEAS
  23. Athanasios Orphanides & Simon van Norden, 2001. "The Unreliability of Output Gap Estimates in Real Time," CIRANO Working Papers 2001s-57, CIRANO.
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