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

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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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    File URL: https://mpra.ub.uni-muenchen.de/34229/1/MPRA_paper_34229.pdf
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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. 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.
    3. Juan Manuel Julio, 2011. "Data Revisions and the Output Gap," Borradores de Economia 642, Banco de la Republica de Colombia.
    4. Juan Manuel Julio Román, 2011. "Modeling Data Revisions," BORRADORES DE ECONOMIA 007929, BANCO DE LA REPÚBLICA.
    5. 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.
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    Cited by:

    1. Andrés González & Segio Ocampo & Julián Pérez & Diego Rodríguez, 2013. "Output Gap and Neutral Interest Measures of Colombia," Monetaria, Centro de Estudios Monetarios Latinoamericanos, CEMLA, vol. 0(2), pages 231-286, July-Dece.
    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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    More about this item

    Keywords

    Business Cycles; Hodrick-Prescott Filter;

    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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