IDEAS home Printed from https://ideas.repec.org/p/vic/vicewp/0406.html
   My bibliography  Save this paper

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

Author

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.

Suggested Citation

  • David E. Giles & Chad N. Stroomer, 2004. "Identifying the Cycle of a Macroeconomic Time-Series Using Fuzzy Filtering," Econometrics Working Papers 0406, Department of Economics, University of Victoria.
    • Handle: RePEc:vic:vicewp:0406
    Note: ISSN 1485-6441
    as

    Download full text from publisher

    File URL: https://www.uvic.ca/socialsciences/economics/_assets/docs/econometrics/ewp0406.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Andrew Rennison, 2003. "Comparing Alternative Output-Gap Estimators: A Monte Carlo Approach," Staff Working Papers 03-8, Bank of Canada.
    4. repec:bla:ecorec:v:73:y:1997:i:222:p:225-32 is not listed on IDEAS
    5. Canova, Fabio, 1998. "Detrending and business cycle facts," Journal of Monetary Economics, Elsevier, vol. 41(3), pages 475-512, May.
    6. Uhlig, H.F.H.V.S. & Ravn, M., 1997. "On Adjusting the H-P Filter for the Frequency of Observations," Other publications TiSEM 1dd22a17-bed0-4e7c-a2c1-d, Tilburg University, School of Economics and Management.
    7. Alasdair Scott, 2000. "Stylised facts from output gap measures," Reserve Bank of New Zealand Discussion Paper Series DP2000/07, Reserve Bank of New Zealand.
    8. Backus, David K & Kehoe, Patrick J, 1992. "International Evidence of the Historical Properties of Business Cycles," American Economic Review, American Economic Association, vol. 82(4), pages 864-888, September.
    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. 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.
    11. Sichel, Daniel E, 1989. "Are Business Cycles Asymmetric? A Correction," Journal of Political Economy, University of Chicago Press, vol. 97(5), pages 1255-1260, October.
    12. Levy, Daniel & Dezhbakhsh, Hashem, 2003. "On the Typical Spectral Shape of an Economic Variable," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 10(7), pages 417-423.
    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 231-247, July-Sept.
    14. 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.
    15. David E. A. Giles, 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 225-232, 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. Alain Guay & Pierre Saint-Amant, 2005. "Do the Hodrick-Prescott and Baxter-King Filters Provide a Good Approximation of Business Cycles?," Annals of Economics and Statistics, GENES, issue 77, pages 133-155.
    18. Zacharias Psaradakis & Martin Sola, 2003. "On detrending and cyclical asymmetry," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(3), pages 271-289.
    19. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
    20. 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.).
    21. 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.
    22. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July.
    23. Randal Verbrugge Randal Verbrugge, 1997. "Investigating Cyclical Asymmetries," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 2(1), pages 1-10, April.
    24. 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.
    25. 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 307-328, April.
    26. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.
    4. Erfani , Alireza & Safari , Solmaz, 2014. "Estimation of Seigniorage Laffer curve in Iran: A Fuzzy C-Means Clustering Framework," Journal of Money and Economy, Monetary and Banking Research Institute, Central Bank of the Islamic Republic of Iran, vol. 9(1), pages 93-115, October.
    5. Hui Feng, 2011. "Forecasting comparison between two nonlinear models: fuzzy regression versus SETAR," Applied Economics Letters, Taylor & Francis Journals, vol. 18(17), pages 1623-1627.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zacharias Psaradakis & Martin Sola, 2003. "On detrending and cyclical asymmetry," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(3), pages 271-289.
    2. 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.
    3. Sergey Sinelnikov-Murylev & Sergey Drobyshevsky & Maria Kazakova & Michael Alexeev, 2016. "Decomposition of Russia's GDP Growth Rates," Research Paper Series, Gaidar Institute for Economic Policy, issue 167P, pages 123-123.
    4. Maravall, A. & del Rio, A., 2007. "Temporal aggregation, systematic sampling, and the Hodrick-Prescott filter," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 975-998, October.
    5. Odile Chagny & Jörg Döpke, 2001. "Measures of the Output Gap in the Euro-Zone: An Empirical Assessment of Selected Methods," Vierteljahrshefte zur Wirtschaftsforschung / Quarterly Journal of Economic Research, DIW Berlin, German Institute for Economic Research, vol. 70(3), pages 310-332.
    6. Zsolt Darvas & Gábor Vadas, 2003. "Univariate Potential Output Estimations for Hungary," MNB Working Papers 2003/8, Magyar Nemzeti Bank (Central Bank of Hungary).
    7. Fukuda, Kosei, 2012. "Illustrating extraordinary shocks causing trend breaks," Economic Modelling, Elsevier, vol. 29(4), pages 1045-1052.
    8. Ard den Reijer, 2006. "The Dutch business cycle: which indicators should we monitor?," DNB Working Papers 100, Netherlands Central Bank, Research Department.
    9. Leo Butler, 1996. "The Bank of Canada's New Quarterly Porjection Model Part 4 : A Semi- Structural Method to Estimate Potential Output : Combining Economic Theory with a Time-Series Filter," Technical Reports 77, Bank of Canada.
    10. Galimberti, Jaqueson K. & Moura, Marcelo L., 2016. "Improving the reliability of real-time output gap estimates using survey forecasts," International Journal of Forecasting, Elsevier, vol. 32(2), pages 358-373.
    11. L.A. Gil-Alana, 2005. "Fractional Cyclical Structures & Business Cycles in the Specification of the US Real Output," European Research Studies Journal, European Research Studies Journal, vol. 0(1-2), pages 99-126.
    12. Aadland, David, 2005. "Detrending time-aggregated data," Economics Letters, Elsevier, vol. 89(3), pages 287-293, December.
    13. Ahsan ul Haq Satti & Wasim Shahid Malik, 2017. "The Unreliability of Output-Gap Estimates in Real Time," The Pakistan Development Review, Pakistan Institute of Development Economics, vol. 56(3), pages 193-219.
    14. Andrikopoulos, Andreas & Loizides, Ioannis & Prodromidis, Kyprianos, 2004. "Fiscal policy and political business cycles in the EU," European Journal of Political Economy, Elsevier, vol. 20(1), pages 125-152, March.
    15. Odia Ndongo, Yves Francis, 2006. "Datation du Cycle du PIB Camerounais entre 1960 et 2003," MPRA Paper 552, University Library of Munich, Germany.
    16. Fritz, Marlon, 2019. "Steady state adjusting trends using a data-driven local polynomial regression," Economic Modelling, Elsevier, vol. 83(C), pages 312-325.
    17. Robert J. Hodrick, 2020. "An Exploration of Trend-Cycle Decomposition Methodologies in Simulated Data," NBER Working Papers 26750, National Bureau of Economic Research, Inc.
    18. S. Adnan H. A. S. Bukhari & Safdar Ullah Khan, 2008. "Estimating Output Gap for Pakistan Economy: Structural and Statistical Approaches," SBP Research Bulletin, State Bank of Pakistan, Research Department, vol. 4, pages 31-60.
    19. 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.
    20. Alain Guay & Pierre Saint-Amant, 2005. "Do the Hodrick-Prescott and Baxter-King Filters Provide a Good Approximation of Business Cycles?," Annals of Economics and Statistics, GENES, issue 77, pages 133-155.

    More about this item

    Keywords

    Fuzzy filter; fuzzy clustering; business cycle; trend extraction; HP filter;
    All these keywords.

    JEL classification:

    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:vic:vicewp:0406. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Kali Moon (email available below). General contact details of provider: https://edirc.repec.org/data/devicca.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.