IDEAS home Printed from https://ideas.repec.org/a/jns/jbstat/v235y2015i6p518-538.html
   My bibliography  Save this article

Why We Should Use High Values for the Smoothing Parameter of the Hodrick-Prescott Filter

Author

Listed:
  • Flaig Gebhard

    (University of Munich, Schackstraße 4, 80539 Munich, Germany)

Abstract

The HP filter is the most popular filter for extracting the unobserved trend and cycle components from a time series. Many researchers consider the smoothing parameter λ = 1600 as something like a universal constant. It is well known that the HP filter is an optimal filter under some restrictive assumptions, especially that the “cycle” is white noise. In this paper we show that we can get a good approximation of the optimal Wiener-Kolmogorov filter for autocorrelated cycle components by using the HP filter with a much higher smoothing parameter than commonly used. In addition, a new method - based on the properties of the differences of the estimated trend - is proposed for the selection of the smoothing parameter.

Suggested Citation

  • Flaig Gebhard, 2015. "Why We Should Use High Values for the Smoothing Parameter of the Hodrick-Prescott Filter," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 235(6), pages 518-538, December.
    • Handle: RePEc:jns:jbstat:v:235:y:2015:i:6:p:518-538
    DOI: 10.1515/jbnst-2015-0602
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/jbnst-2015-0602
    Download Restriction: no
    File URL: https://libkey.io/10.1515/jbnst-2015-0602?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Andreas Blöchl & Gebhard Flaig, 2014. "The Hodrick-Prescott Filter with a Time-Varying Penalization Parameter. An Application for the Trend Estimation of Global Temperature," CESifo Working Paper Series 4577, CESifo.
    3. 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.
    4. Proietti, Tommaso, 2007. "Signal extraction and filtering by linear semiparametric methods," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 935-958, October.
    5. 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.
    6. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July.
    7. 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.
    8. 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.
    9. Tommaso Proietti, 2005. "Forecasting and signal extraction with misspecified models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 24(8), pages 539-556.
    10. Morten O. Ravn & Harald Uhlig, 2002. "On adjusting the Hodrick-Prescott filter for the frequency of observations," The Review of Economics and Statistics, MIT Press, vol. 84(2), pages 371-375.
    11. McElroy, Tucker, 2008. "Matrix Formulas For Nonstationary Arima Signal Extraction," Econometric Theory, Cambridge University Press, vol. 24(4), pages 988-1009, August.
    12. Harvey, Andrew C. & Delle Monache, Davide, 2009. "Computing the mean square error of unobserved components extracted by misspecified time series models," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 283-295, February.
    13. Pedersen, Torben Mark, 2001. "The Hodrick-Prescott filter, the Slutzky effect, and the distortionary effect of filters," Journal of Economic Dynamics and Control, Elsevier, vol. 25(8), pages 1081-1101, August.
    14. George E. P. Box & Steven C. Hillmer & George C. Tiao, 1978. "Analysis and Modeling of Seasonal Time Series," NBER Chapters, in: Seasonal Analysis of Economic Time Series, pages 309-344, National Bureau of Economic Research, Inc.
    15. Gomez, Victor, 1999. "Three Equivalent Methods for Filtering Finite Nonstationary Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 109-116, January.
    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. Crafts, Nicholas & Mills, Terence C., 2019. "The Pre-1914 UK Productivity Slowdown: A Reappraisal," CAGE Online Working Paper Series 437, Competitive Advantage in the Global Economy (CAGE).
    2. Leibfritz, Willi & Rottmann, Horst, 2013. "Fiscal policy during business cycles in developing countries: The case of Africa," Weidener Diskussionspapiere 36, University of Applied Sciences Amberg-Weiden (OTH).
    3. Bloechl, Andreas, 2014. "Reducing the Excess Variability of the Hodrick-Prescott Filter by Flexible Penalization," Discussion Papers in Economics 17940, University of Munich, Department of Economics.
    4. Blöchl, Andreas, 2014. "Penalized Splines as Frequency Selective Filters - Reducing the Excess Variability at the Margins," Discussion Papers in Economics 20687, University of Munich, Department of Economics.
    5. Bloechl, Andreas, 2014. "Penalized Splines, Mixed Models and the Wiener-Kolmogorov Filter," Discussion Papers in Economics 21406, University of Munich, Department of Economics.
    6. Nicholas Crafts & Terence C. Mills, 2017. "Six centuries of British economic growth: a time-series perspective," European Review of Economic History, European Historical Economics Society, vol. 21(2), pages 141-158.
    7. Yoon, Gawon, 2015. "Locating change-points in Hodrick–Prescott trends with an application to US real GDP: A generalized unobserved components model approach," Economic Modelling, Elsevier, vol. 45(C), pages 136-141.
    8. Willi Leibfritz & Gebhard Flaig, 2013. "Economic Growth in Africa: Comparing Recent Improvements with the "lost 1980s and early 1990s" and Estimating New Growth Trends," CESifo Working Paper Series 4215, CESifo.
    9. Sebastian Letmathe, 2022. "Data-driven P-Splines under short-range dependence," Working Papers CIE 152, Paderborn University, CIE Center for International Economics.

    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. Jaqueson K. Galimberti & Marcelo L. Moura, 2011. "Improving the reliability of real-time Hodrick-Prescott filtering using survey forecasts," Centre for Growth and Business Cycle Research Discussion Paper Series 159, Economics, The University of Manchester.
    2. Tawadros, George B., 2011. "The stylised facts of Australia's business cycle," Economic Modelling, Elsevier, vol. 28(1), pages 549-556.
    3. 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.
    4. Gregory, Allan W. & Smith, Gregor W., 1996. "Measuring business cycles with business-cycle models," Journal of Economic Dynamics and Control, Elsevier, vol. 20(6-7), pages 1007-1025.
    5. Blonigen, Bruce A. & Piger, Jeremy & Sly, Nicholas, 2014. "Comovement in GDP trends and cycles among trading partners," Journal of International Economics, Elsevier, vol. 94(2), pages 239-247.
    6. James D. Hamilton, 2017. "Why You Should Never Use the Hodrick-Prescott Filter," NBER Working Papers 23429, National Bureau of Economic Research, Inc.
    7. Mr. Andreas Billmeier, 2004. "Ghostbusting: Which Output Gap Measure Really Matters?," IMF Working Papers 2004/146, International Monetary Fund.
    8. Robert J. Hodrick, 2020. "An Exploration of Trend-Cycle Decomposition Methodologies in Simulated Data," NBER Working Papers 26750, National Bureau of Economic Research, Inc.
    9. 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.
    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. 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.
    12. 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.
    13. 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.
    14. Kozicki, Sharon, 1999. "Multivariate detrending under common trend restrictions: Implications for business cycle research," Journal of Economic Dynamics and Control, Elsevier, vol. 23(7), pages 997-1028, June.
    15. Roberto Iannaccone & Edoardo Otranto, 2003. "Signal Extraction in Continuous Time and the Generalized Hodrick- Prescott Filter," Econometrics 0311002, University Library of Munich, Germany.
    16. Carnazza, Giovanni & Liberati, Paolo & Sacchi, Agnese, 2020. "The cyclically-adjusted primary balance: A novel approach for the euro area," Journal of Policy Modeling, Elsevier, vol. 42(5), pages 1123-1145.
    17. Fukuda, Kosei, 2012. "Illustrating extraordinary shocks causing trend breaks," Economic Modelling, Elsevier, vol. 29(4), pages 1045-1052.
    18. Willie Lahari, 2011. "Assessing Business Cycle Synchronisation - Prospects for a Pacific Islands Currency Union," Working Papers 1110, University of Otago, Department of Economics, revised Oct 2011.
    19. Alain Guay & Pierre St-Amant, 1996. "Do Mechanical Filters Provide a Good Approximation of Business Cycles?," Technical Reports 78, Bank of Canada.
    20. Ard den Reijer, 2006. "The Dutch business cycle: which indicators should we monitor?," DNB Working Papers 100, Netherlands Central Bank, Research Department.

    More about this item

    Keywords

    Hodrick-Prescott filter; Wiener-Kolmogorov filter; smoothing parameter; trends; 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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

    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:jns:jbstat:v:235:y:2015:i:6:p:518-538. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    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.