IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/2005.html
   My bibliography  Save this paper

Business Cycles, Trend Elimination, and the HP Filter

Author

Abstract

We analyze trend elimination methods and business cycle estimation by data filtering of the type introduced by Whittaker (1923) and popularized in economics in a particular form by Hodrick and Prescott (1980/1997; HP). A limit theory is developed for the HP filter for various classes of stochastic trend, trend break, and trend stationary data. Properties of the filtered series are shown to depend closely on the choice of the smoothing parameter (lambda). For instance, when lambda = O(n^4) where n is the sample size, and the HP filter is applied to an I(1) process, the filter does not remove the stochastic trend in the limit as n approaches infinity. Instead, the filter produces a smoothed Gaussian limit process that is differentiable to the 4'th order. The residual 'cyclical' process has the random wandering non-differentiable characteristics of Brownian motion, thereby explaining the frequently observed 'spurious cycle' effect of the HP filter. On the other hand, when lambda = o(n), the filter reproduces the limit Brownian motion and eliminates the stochastic trend giving a zero 'cyclical' process. Simulations reveal that the lambda = O(n^4) limit theory provides a good approximation to the actual HP filter for sample sizes common in practical work. When it is used as a trend removal device, the HP filter therefore typically fails to eliminate stochastic trends, contrary to what is now standard belief in applied macroeconomics. The findings are related to recent public debates about the long run effects of the global financial crisis.

Suggested Citation

  • Peter C. B. Phillips & Sainan Jin, 2015. "Business Cycles, Trend Elimination, and the HP Filter," Cowles Foundation Discussion Papers 2005, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:2005
    as

    Download full text from publisher

    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d20/d2005.pdf
    Download Restriction: no

    Citations

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


    Cited by:

    1. Jiti Gao & Oliver Linton & Bin Peng, 2017. "Inference on a Semiparametric Model with Global Power Law and Local Nonparametric Trends," Monash Econometrics and Business Statistics Working Papers 10/17, Monash University, Department of Econometrics and Business Statistics.
    2. Hendrickson, Joshua R. & Salter, Alexander William, 2016. "Money, liquidity, and the structure of production," Journal of Economic Dynamics and Control, Elsevier, vol. 73(C), pages 314-328.
    3. Ingrid Groessl & Artur Tarassow, 2015. "A Microfounded Model of Money Demand Under Uncertainty, and some Empirical Evidence," Macroeconomics and Finance Series 201504, Hamburg University, Department Wirtschaft und Politik, revised Jan 2018.
    4. AMENDOLA, Adalgiso & DI SERIO, Mario & FRAGETTA, Matteo, 2018. "The Government Spending Multiplier at the Zero Lower Bound: Evidence from the Euro Area," CELPE Discussion Papers 153, CELPE - Centre of Labour Economics and Economic Policy, University of Salerno, Italy.
    5. repec:eee:inecon:v:109:y:2017:i:c:p:43-67 is not listed on IDEAS
    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. Kovačić, Zlatko & Vilotić, Miloš, 2017. "Assessing European business cycles synchronization," MPRA Paper 79990, University Library of Munich, Germany.
    8. Özer Karagedikli & Dr John McDermott, 2016. "Inflation expectations and low inflation in New Zealand," Reserve Bank of New Zealand Discussion Paper Series DP2016/09, Reserve Bank of New Zealand.

    More about this item

    Keywords

    Detrending; Graduation; Hodrick Prescott filter; Integrated process; Limit theory; Smoothing; Trend break; Whittaker filter;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

    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:cwl:cwldpp:2005. 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: (Matthew Regan). General contact details of provider: http://edirc.repec.org/data/cowleus.html .

    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.

    We have no references for this item. You can help adding them by using 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.

    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.