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The Hodrick-Prescott filter with priors: linear restrictions on HP filters

Author

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  • Julio Roman, Juan Manuel

Abstract

A closed formula for the Hodrick & Prescott, HP, filter subject to linear restrictions is derived. This filter is also known as the HP filter with priors. When the formula is applied to the ordinary HP filter linear restrictions apply only within the sample. However, when this formula is applied to the extended HP filter and extensions that correct for GDP revisions and delays, linear restrictions apply out of sample also.

Suggested Citation

  • Julio Roman, Juan Manuel, 2011. "The Hodrick-Prescott filter with priors: linear restrictions on HP filters," MPRA Paper 34202, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:34202
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    References listed on IDEAS

    as
    1. Kaiser, Regina & Maravall, Agustin, 2005. "Combining filter design with model-based filtering (with an application to business-cycle estimation)," International Journal of Forecasting, Elsevier, vol. 21(4), pages 691-710.
    2. Juan Manuel Julio, 2011. "Data Revisions and the Output Gap," Borradores de Economia 7956, Banco de la Republica.
    3. Regina Kaiser & Agustín Maravall, 1999. "Estimation of the business cycle: A modified Hodrick-Prescott filter," Spanish Economic Review, Springer;Spanish Economic Association, vol. 1(2), pages 175-206.
    4. 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.
    5. Juan Manuel Julio, 2011. "Modeling Data Revisions," Borradores de Economia 641, Banco de la Republica de Colombia.
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    Cited by:

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    2. Kristian Jönsson, 2018. "Extending the state-space representation of the judgement-augmented Hodrick-Prescott filter," Economics Bulletin, AccessEcon, vol. 38(1), pages 623-628.

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    Keywords

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    JEL classification:

    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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