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

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Abstract

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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Bibliographic Info

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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Keywords: Fuzzy filter; fuzzy clustering; business cycle; trend extraction; HP filter;

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References

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  1. Athanasios Orphanides & Simon van Norden, 2002. "The Unreliability of Output-Gap Estimates in Real Time," The Review of Economics and Statistics, MIT Press, vol. 84(4), pages 569-583, November.
  2. 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.
  3. Daniel Levy & Hashem Dezhbakhsh, 2002. "On the Typical Spectral Shape of an Economic Variable," Emory Economics 0203, Department of Economics, Emory University (Atlanta).
  4. 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.
  5. 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.
  6. 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.
  7. Uhlig, H.F.H.V.S. & Ravn, M., 1997. "On Adjusting the H-P Filter for the Frequency of Observations," Discussion Paper 1997-50, Tilburg University, Center for Economic Research.
  8. 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.
  9. 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.
  10. Zacharias Psaradakis & Martin Sola, 2003. "On detrending and cyclical asymmetry," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(3), pages 271-289.
  11. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July.
  12. Canova, Fabio, 1998. "Detrending and business cycle facts," Journal of Monetary Economics, Elsevier, vol. 41(3), pages 475-512, May.
  13. Randal Verbrugge Randal Verbrugge, 1997. "Investigating Cyclical Asymmetries," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 2(1), pages 1-10, April.
  14. Andrew Rennison, 2003. "Comparing Alternative Output-Gap Estimators: A Monte Carlo Approach," Working Papers 03-8, Bank of Canada.
  15. 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.).
  16. Alain Guay & Pierre St-Amant, 1997. "Do the Hodrick-Prescott and Baxter-King Filters Provide a Good Approximation of Business Cycles?," Cahiers de recherche CREFE / CREFE Working Papers 53, CREFE, Université du Québec à Montréal.
  17. Alasdair Scott, 2000. "Stylised facts from output gap measures," Reserve Bank of New Zealand Discussion Paper Series DP2000/07, Reserve Bank of New Zealand.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. 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.
  23. 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.
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Cited by:
  1. knani, ramzi & fredj, ali, 2010. "Mondialisation et fluctuations des cycles économiques
    [globalisation and business cycle fluctuation]
    ," MPRA Paper 22755, University Library of Munich, Germany.
  2. Hui Feng & David E. Giles, 2007. "Bayesian Fuzzy Regression Analysis and Model Selection: Theory and Evidence," Econometrics Working Papers 0710, Department of Economics, University of Victoria.
  3. Shepherd, David & Shi, Francis K.C., 2006. "Fuzzy modelling and estimation of economic relationships," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 417-433, November.

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