IDEAS home Printed from https://ideas.repec.org/p/cam/camdae/0113.html
   My bibliography  Save this paper

General Model-based Filters for Extracting Cycles and Trends in Economic Time Series

Author

Listed:
  • Harvey, A.C.
  • Trimbur, T.M.

Abstract

A new class of model-based filters for extracting trends and cycles in economic time series is presented. These low pass and band pass filters are derived in a mutually consistent manner as the joint solution to a signal extraction problem in an unobserved components model. The resulting trends and cycles are computed in finite samples using a Kalman filter and associated smoother. The filters form a class which is a generalisation of the class of Butterworth filters, widely used in engineering. They are very flexible and have the important property of allowing relatively smooth cycles to be extracted from economic time series. Perfectly sharp, or ideal, band pass filters emerge as a special case. Applying the method to a quarterly series on US investment shows a clearly defined cycle currently at the peak of a boom.

Suggested Citation

  • 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.
  • Handle: RePEc:cam:camdae:0113
    Note: EM
    as

    Download full text from publisher

    File URL: http://www.econ.cam.ac.uk/research-files/repec/cam/pdf/wp0113.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    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. 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.
    3. 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.
    4. Koopman, Siem Jan & Harvey, Andrew, 2003. "Computing observation weights for signal extraction and filtering," Journal of Economic Dynamics and Control, Elsevier, vol. 27(7), pages 1317-1333, May.
    5. 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, May.
    6. Luca Benati, 2001. "Band-pass filtering, cointegration, and business cycle analysis," Bank of England working papers 142, Bank of England.
    Full references (including those not matched with items on IDEAS)

    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. Alessandra Iacobucci, 2003. "Spectral Analysis for Economic Time Series," Documents de Travail de l'OFCE 2003-07, Observatoire Francais des Conjonctures Economiques (OFCE).
    2. Cuddington, John T. & Nülle, Grant, 2014. "Variable long-term trends in mineral prices: The ongoing tug-of-war between exploration, depletion, and technological change," Journal of International Money and Finance, Elsevier, vol. 42(C), pages 224-252.
    3. Strohsal, Till & Proaño, Christian R. & Wolters, Jürgen, 2019. "Characterizing the financial cycle: Evidence from a frequency domain analysis," Journal of Banking & Finance, Elsevier, vol. 106(C), pages 568-591.
    4. Thomas M. Trimbur, 2006. "Detrending economic time series: a Bayesian generalization of the Hodrick-Prescott filter," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(4), pages 247-273.
    5. 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.
    6. Arturo Estrella, 2007. "Extracting business cycle fluctuations: what do time series filters really do?," Staff Reports 289, Federal Reserve Bank of New York.
    7. 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.
    8. Proietti, Tommaso, 2007. "Signal extraction and filtering by linear semiparametric methods," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 935-958, October.
    9. Sun Xiaojin & Tsang Kwok Ping, 2019. "What cycles? Data detrending in DSGE models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 23(3), pages 1-23, June.
    10. Alessandra Iacobucci & Alain Noullez, 2005. "A Frequency Selective Filter for Short-Length Time Series," Computational Economics, Springer;Society for Computational Economics, vol. 25(1), pages 75-102, February.
    11. Faria, Gonçalo & Verona, Fabio, 2020. "The yield curve and the stock market: Mind the long run," Journal of Financial Markets, Elsevier, vol. 50(C).
    12. 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.
    13. Lubos Hanus & Lukas Vacha, 2015. "Business cycle synchronization of the Visegrad Four and the European Union," Working Papers IES 2015/19, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Jul 2015.
    14. Polanski, Arnold & Stoja, Evarist, 2017. "Forecasting multidimensional tail risk at short and long horizons," International Journal of Forecasting, Elsevier, vol. 33(4), pages 958-969.
    15. Luca Benati, 2001. "Band-pass filtering, cointegration, and business cycle analysis," Bank of England working papers 142, Bank of England.
    16. Richard Ashley & Randal Verbrugge, 2009. "Frequency Dependence in Regression Model Coefficients: An Alternative Approach for Modeling Nonlinear Dynamic Relationships in Time Series," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 4-20.
    17. Henk Kranendonk & Jan Bonenkamp & Johan Verbruggen, 2004. "A leading indicator for the Dutch economy; methodological and empirical revision of the CPB system," CPB Discussion Paper 32, CPB Netherlands Bureau for Economic Policy Analysis.
    18. Günes Kamber & James Morley & Benjamin Wong, 2018. "Intuitive and Reliable Estimates of the Output Gap from a Beveridge-Nelson Filter," The Review of Economics and Statistics, MIT Press, vol. 100(3), pages 550-566, July.
    19. Öğünç, Fethi & Akdoğan, Kurmaş & Başer, Selen & Chadwick, Meltem Gülenay & Ertuğ, Dilara & Hülagü, Timur & Kösem, Sevim & Özmen, Mustafa Utku & Tekatlı, Necati, 2013. "Short-term inflation forecasting models for Turkey and a forecast combination analysis," Economic Modelling, Elsevier, vol. 33(C), pages 312-325.
    20. Tripier, Fabien, 2006. "Sticky prices, fair wages, and the co-movements of unemployment and labor productivity growth," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2749-2774, December.

    More about this item

    Keywords

    band pass filter; Butterworth filter; ideal filter; Kalman filter; signal extraction; unobserved components;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    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:cam:camdae:0113. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://www.econ.cam.ac.uk/ .

    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: Jake Dyer (email available below). General contact details of provider: https://www.econ.cam.ac.uk/ .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.