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Constructing Confidence Bands for the Hodrick-Prescott Filter



By noting that the Hodrick-Prescott filter can be expressed as the solution to a particular regression problem, we are able to show how to construct confidence bands for the filtered time-series. This procedure requires that the data are stationary. The construction of such confidence bands is illustrated using annual U.S. data for real value-added output; and monthly U.S. data for the unemployment rate.

Suggested Citation

  • David E. Giles, 2012. "Constructing Confidence Bands for the Hodrick-Prescott Filter," Econometrics Working Papers 1202, Department of Economics, University of Victoria.
  • Handle: RePEc:vic:vicewp:1202 Note: ISSN 1485-6441

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    References listed on IDEAS

    1. Polasek, Wolfgang, 2011. "The Hodrick-Prescott (HP) Filter as a Bayesian Regression Model," Economics Series 277, Institute for Advanced Studies.
    2. Danthine, Jean-Pierre & Girardin, Michel, 1989. "Business cycles in Switzerland : A comparative study," European Economic Review, Elsevier, vol. 33(1), pages 31-50, January.
    3. Schlicht, Ekkehart, 2004. "Estimating the Smoothing Parameter in the So-Called Hodrick-Prescott Filter," IZA Discussion Papers 1054, Institute for the Study of Labor (IZA).
    4. 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.
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    Blog mentions

    As found by, the blog aggregator for Economics research:
    1. More on Confidence Bands for the HP Filter
      by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2012-04-20 20:25:00
    2. More on Confidence Bands for the HP Filter
      by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2012-04-20 20:25:00
    3. Hodrick-Prescott Filter Paper
      by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2012-07-16 23:32:00

    More about this item


    Hodrick-Prescott filter; time-series decomposition; confidence bands;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles

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