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


  • Flaig Gebhard

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


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

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    References listed on IDEAS

    1. 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.
    2. 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.
    3. George E. P. Box & Steven Hillmer & George C. Tiao, 1979. "Analysis and Modeling of Seasonal Time Series," NBER Chapters,in: Seasonal Analysis of Economic Time Series, pages 309-346 National Bureau of Economic Research, Inc.
    4. Tommaso Proietti, 2005. "Forecasting and signal extraction with misspecified models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 24(8), pages 539-556.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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 Group Munich.
    11. 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.
    12. Proietti, Tommaso, 2007. "Signal extraction and filtering by linear semiparametric methods," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 935-958, October.
    13. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July.
    14. 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.
    15. McElroy, Tucker, 2008. "Matrix Formulas For Nonstationary Arima Signal Extraction," Econometric Theory, Cambridge University Press, vol. 24(04), pages 988-1009, August.
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    Cited by:

    1. 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).
    2. 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.
    3. 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 Group Munich.
    4. 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.

    More about this item


    Hodrick-Prescott filter; Wiener-Kolmogorov filter; smoothing parameter; trends; cycles;

    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


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