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Exact formulas for the Hodrick-Prescott filter

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  • Tucker McElroy

Abstract

The Hodrick--Prescott (HP) filter is widely used in the field of economics to estimate trends and cycles from time series data. For certain applications--such as deriving implied trend and cycle models and obtaining filter weights--it is desirable to express the frequency response of the HP as the spectral density of an ARMA model; in other words, to accomplish the spectral factorization of the HP filter. This paper presents an exact approach to this problem, which makes it possible to provide exact algebraic formulas for the HP filter coefficients in terms of the HP's signal-to-noise ratio. Copyright Royal Economic Society 2008

Suggested Citation

  • Tucker McElroy, 2008. "Exact formulas for the Hodrick-Prescott filter," Econometrics Journal, Royal Economic Society, vol. 11(1), pages 209-217, March.
  • Handle: RePEc:ect:emjrnl:v:11:y:2008:i:1:p:209-217
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    Cited by:

    1. Coeurdacier, Nicolas & Kollmann, Robert & Martin, Philippe, 2010. "International portfolios, capital accumulation and foreign assets dynamics," Journal of International Economics, Elsevier, vol. 80(1), pages 100-112, January.
    2. Henry R. Hyatt & Tucker S. McElroy, 2017. "Labor Reallocation, Employment, and Earnings: Vector Autoregression Evidence," Working Papers 17-11, Center for Economic Studies, U.S. Census Bureau.
    3. McElroy, Tucker & Wildi, Marc, 2013. "Multi-step-ahead estimation of time series models," International Journal of Forecasting, Elsevier, vol. 29(3), pages 378-394.
    4. Nicolas Coeurdacier, 2011. "Limited participation and International Risk-Sharing," 2011 Meeting Papers 613, Society for Economic Dynamics.
    5. Kristian Jönsson, 2010. "Trend extraction with a judgement-augmented hodrick–prescott filter," Empirical Economics, Springer, vol. 39(3), pages 703-711, December.
    6. Wildi Marc & McElroy Tucker, 2016. "Optimal Real-Time Filters for Linear Prediction Problems," Journal of Time Series Econometrics, De Gruyter, vol. 8(2), pages 155-192, July.
    7. James D. Hamilton, 2017. "Why You Should Never Use the Hodrick-Prescott Filter," NBER Working Papers 23429, National Bureau of Economic Research, Inc.
    8. repec:spo:wpecon:info:hdl:2441/c8dmi8nm4pdjkuc9g7084aa4m is not listed on IDEAS

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