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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

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File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1368-423X.2008.00230.x
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Bibliographic Info

Article provided by Royal Economic Society in its journal Econometrics Journal.

Volume (Year): 11 (2008)
Issue (Month): 1 (03)
Pages: 209-217

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Handle: RePEc:ect:emjrnl:v:11:y:2008:i:1:p:209-217

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Cited by:
  1. Kristian Jönsson, 2010. "Trend extraction with a judgement-augmented hodrick–prescott filter," Empirical Economics, Springer, vol. 39(3), pages 703-711, December.
  2. Robert Kollmann & Nicolas Coeurdacier & Philippe Martin, 2010. "International portfolios, capital accumulation and foreign assets dynamics," Sciences Po publications info:hdl:2441/c8dmi8nm4pd, Sciences Po.
  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. repec:spo:wpecon:info:hdl:2441/c8dmi8nm4pdjkuc9g7084aa4m is not listed on IDEAS

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