IDEAS home Printed from https://ideas.repec.org/a/seb/journl/v3y2005i1p79-96.html
   My bibliography  Save this article

Is "The ideal filter" really Ideal: The usage of Frequency Filtering and Spurious Cycles

Author

Listed:
  • Lyubomir Ivanov

    (Tsenov Academy of Economics)

Abstract

In this paper the filter of Hodrick and Prescott, the band-pass filter of Baxter and King, "the ideal filter" and the first-differencing are analyzed. It is shown that ideal filters are able to produce spurious cycles not only when a unit root is present in the data but also when the root is less than unity. The main critiques of first-differencing are outlined and further analyzed. The conclusion is that differencing and more generally methods in conformity with the underlying properties of non-stationary series are the preferable choice. At the same time the application of ideal filters and their approximations (including HP and BP) is very dangerous and their usage is to be avoided.

Suggested Citation

  • Lyubomir Ivanov, 2005. "Is "The ideal filter" really Ideal: The usage of Frequency Filtering and Spurious Cycles," South-Eastern Europe Journal of Economics, Association of Economic Universities of South and Eastern Europe and the Black Sea Region, vol. 3(1), pages 79-96.
    • Handle: RePEc:seb:journl:v:3:y:2005:i:1:p:79-96
    as

    Download full text from publisher

    File URL: http://www.asecu.gr/Seeje/issue04/ivanov.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Murray, Christian J. & Nelson, Charles R., 2000. "The uncertain trend in U.S. GDP," Journal of Monetary Economics, Elsevier, vol. 46(1), pages 79-95, August.
    2. 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.
    3. Robert J. Gordon, 1986. "The American Business Cycle: Continuity and Change," NBER Books, National Bureau of Economic Research, Inc, number gord86-1.
    4. Nelson, Charles R & Kang, Heejoon, 1981. "Spurious Periodicity in Inappropriately Detrended Time Series," Econometrica, Econometric Society, vol. 49(3), pages 741-751, May.
    5. repec:bla:econom:v:67:y:2000:i:267:p:347-74 is not listed on IDEAS
    6. Shigeyuki Hamori & Shin-Ichi Kitasaka, 1997. "The characteristics of the business cycle in Japan," Applied Economics, Taylor & Francis Journals, vol. 29(9), pages 1105-1113.
    7. Canova, Fabio, 1998. "Detrending and business cycle facts: A user's guide," Journal of Monetary Economics, Elsevier, vol. 41(3), pages 533-540, May.
    8. Zarnowitz, Victor & Ozyildirim, Ataman, 2006. "Time series decomposition and measurement of business cycles, trends and growth cycles," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1717-1739, October.
    9. Canova, Fabio, 1998. "Detrending and business cycle facts," Journal of Monetary Economics, Elsevier, vol. 41(3), pages 475-512, May.
    10. Nilss Olekalns, 2001. "Cyclical asymmetries in Australian macroeconomic data," Applied Economics Letters, Taylor & Francis Journals, vol. 8(3), pages 145-148.
    11. James H. Stock & Mark W. Watson, 1990. "Business Cycle Properties of Selected U.S. Economic Time Series, 1959-1988," NBER Working Papers 3376, National Bureau of Economic Research, Inc.
    12. 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.
    13. Gregory, Allan W & Head, Allen C & Raynauld, Jacques, 1997. "Measuring World Business Cycles," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(3), pages 677-701, August.
    14. Victor Zarnowitz & James H. Stock (ary), 1992. "What is a business cycle?," Proceedings, Federal Reserve Bank of St. Louis, pages 3-83.
    15. Regina Kaiser & Agustín Maravall, 1999. "Estimation of the business cycle: A modified Hodrick-Prescott filter," Spanish Economic Review, Springer;Spanish Economic Association, vol. 1(2), pages 175-206.
    16. Apostolos Serletis & David Krause, 2006. "Nominal Stylized Facts of U.S. Business Cycles," World Scientific Book Chapters, in: Money And The Economy, chapter 2, pages 47-56, World Scientific Publishing Co. Pte. Ltd..
    17. Susanto Basu & Alan M. Taylor, 1999. "Business Cycles in International Historical Perspective," Journal of Economic Perspectives, American Economic Association, vol. 13(2), pages 45-68, Spring.
    18. Schenk-Hoppé Klaus Reiner, 2001. "Economic Growth and Business Cycles: A Critical Comment on Detrending Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 5(1), pages 1-13, April.
    19. Fatas, Antonio, 2000. "Endogenous growth and stochastic trends," Journal of Monetary Economics, Elsevier, vol. 45(1), pages 107-128, February.
    20. Terence C. Mills, 2000. "Business Cycle Volatility and Economic Growth: A Reassessment," Journal of Post Keynesian Economics, Taylor & Francis Journals, vol. 23(1), pages 107-116, September.
    21. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    22. Westlund, Anders H & Ohlen, Sven, 1991. "On Testing for Symmetry in Business Cycles," Empirical Economics, Springer, vol. 16(4), pages 479-502.
    23. Terence Mills, 2001. "Business cycle asymmetry and duration dependence: An international perspective," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(6), pages 713-724.
    24. Hilde Christiane BjÛrnland, 2000. "Detrending methods and stylized facts of business cycles in Norway - an international comparison," Empirical Economics, Springer, vol. 25(3), pages 369-392.
    25. Gomez, Victor, 2001. "The Use of Butterworth Filters for Trend and Cycle Estimation in Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(3), pages 365-373, July.
    26. Andreas Hornstein, 2000. "The business cycle and industry comovement," Economic Quarterly, Federal Reserve Bank of Richmond, issue Win, pages 27-48.
    27. Stock, James H & Watson, Mark W, 1996. "Evidence on Structural Instability in Macroeconomic Time Series Relations," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 11-30, January.
    28. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    29. Michael R. Pakko, 1997. "The business cycle and chain-weighted GDP: has our perspective changed?," Review, Federal Reserve Bank of St. Louis, issue Sep, pages 39-49.
    30. 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.
    31. James H. Stock & Mark W. Watson, 1989. "New Indexes of Coincident and Leading Economic Indicators," NBER Chapters, in: NBER Macroeconomics Annual 1989, Volume 4, pages 351-409, National Bureau of Economic Research, Inc.
    32. Victor Zarnowitz & Geoffrey H. Moore, 1986. "Major Changes in Cyclical Behavior," NBER Chapters, in: The American Business Cycle: Continuity and Change, pages 519-582, National Bureau of Economic Research, Inc.
    33. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    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. Pollock D. S. G., 2013. "Cycles, Syllogisms and Semantics: Examining the Idea of Spurious Cycles," Journal of Time Series Econometrics, De Gruyter, vol. 6(1), pages 81-102, September.

    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. Hall, Viv B & Thomson, Peter, 2022. "A boosted HP filter for business cycle analysis: evidence from New Zealand’s small open economy," Working Paper Series 9473, Victoria University of Wellington, School of Economics and Finance.
    2. Aadland, David, 2005. "Detrending time-aggregated data," Economics Letters, Elsevier, vol. 89(3), pages 287-293, December.
    3. Klaus Reiner Schenk-Hopp�, "undated". "Economic Growth and Business Cycles: A Critical Comment on Detrending Time Series (Revised Version)," IEW - Working Papers 054, Institute for Empirical Research in Economics - University of Zurich.
    4. Schenk-Hoppé Klaus Reiner, 2001. "Economic Growth and Business Cycles: A Critical Comment on Detrending Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 5(1), pages 1-13, April.
    5. 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.
    6. Viv B. Hall & Peter Thomson, 2022. "A boosted HP filter for business cycle analysis:evidence from New Zealand's small open economy," CAMA Working Papers 2022-45, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    7. Luca Benati, 2001. "Band-pass filtering, cointegration, and business cycle analysis," Bank of England working papers 142, Bank of England.
    8. Perron, Pierre & Wada, Tatsuma, 2009. "Let's take a break: Trends and cycles in US real GDP," Journal of Monetary Economics, Elsevier, vol. 56(6), pages 749-765, September.
    9. Ghate, Chetan & Pandey, Radhika & Patnaik, Ila, 2013. "Has India emerged? Business cycle stylized facts from a transitioning economy," Structural Change and Economic Dynamics, Elsevier, vol. 24(C), pages 157-172.
    10. Fritz, Marlon, 2019. "Steady state adjusting trends using a data-driven local polynomial regression," Economic Modelling, Elsevier, vol. 83(C), pages 312-325.
    11. Guisinger, Amy Y., 2020. "Gender differences in the volatility of work hours and labor demand," Journal of Macroeconomics, Elsevier, vol. 66(C).
    12. Álvarez, Luis J. & Gómez-Loscos, Ana, 2018. "A menu on output gap estimation methods," Journal of Policy Modeling, Elsevier, vol. 40(4), pages 827-850.
    13. João Valle e Azevedo, 2007. "Interpretation of the Effects of Filtering Integrated Time Series," Working Papers w200712, Banco de Portugal, Economics and Research Department.
    14. Mark Meyer & Peter Winker*, 2005. "Using HP Filtered Data for Econometric Analysis: Some Evidence from Monte Carlo Simulations," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 89(3), pages 303-320, August.
    15. Movshuk, Oleksandr, 2003. "Does the choice of detrending method matter in demand analysis?," Japan and the World Economy, Elsevier, vol. 15(3), pages 341-359, August.
    16. Ángel Guillén & Gabriel Rodríguez, 2014. "Trend-cycle decomposition for Peruvian GDP: application of an alternative method," Latin American Economic Review, Springer;Centro de Investigaciòn y Docencia Económica (CIDE), vol. 23(1), pages 1-44, December.
    17. Fukuda, Kosei, 2012. "Illustrating extraordinary shocks causing trend breaks," Economic Modelling, Elsevier, vol. 29(4), pages 1045-1052.
    18. Jakob De Haan & Robert Inklaar & Richard Jong‐A‐Pin, 2008. "Will Business Cycles In The Euro Area Converge? A Critical Survey Of Empirical Research," Journal of Economic Surveys, Wiley Blackwell, vol. 22(2), pages 234-273, April.
    19. Yi-Ting Chen, 2021. "A mixed-frequency smooth measure for business conditions," Empirical Economics, Springer, vol. 61(4), pages 1699-1724, October.
    20. Eduardo Loría & Emmanuel Salas, 2014. "Ciclos, crecimiento económico y crisis en México, 1980.1-2013.4," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 29(2), pages 131-161.

    More about this item

    Keywords

    Frequency filtering; Hodrick-Prescott filter; Band-Pass Filter; Spurious Cycles;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    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:seb:journl:v:3:y:2005:i:1:p:79-96. 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: Ms. Melina Petromelidou (email available below). General contact details of provider: https://edirc.repec.org/data/asecuea.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.