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The Explicit Formula for the Hodrick-Prescott Filter in a Finite Sample

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  • Adriana Cornea-Madeira

    (University of York)

Abstract

We derive the exact expression for the weights of the Hodrick-Prescott (HP) filter in a finite sample without making any assumptions about the statistical properties of the time series. We use the results to give insights into the properties of the HP filter and to build a fast algorithm with computational improvements by a factor of up to three times in samples typical in economics.

Suggested Citation

  • Adriana Cornea-Madeira, 2017. "The Explicit Formula for the Hodrick-Prescott Filter in a Finite Sample," The Review of Economics and Statistics, MIT Press, vol. 99(2), pages 314-318, May.
    • Handle: RePEc:tpr:restat:v:99:y:2017:i:2:p:314-318
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    Cited by:

    1. Mikael Bask & João Madeira, 2021. "Extrapolative expectations and macroeconomic dynamics: Evidence from an estimated DSGE model," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(1), pages 1101-1111, January.
    2. Peter C. B. Phillips & Zhentao Shi, 2021. "Boosting: Why You Can Use The Hp Filter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(2), pages 521-570, May.
    3. Kristian Jönsson, 2020. "Real-time US GDP gap properties using Hamilton’s regression-based filter," Empirical Economics, Springer, vol. 59(1), pages 307-314, July.
    4. Peter C.B. Phillips & Zhentao Shi, 2019. "Boosting the Hodrick-Prescott Filter," Cowles Foundation Discussion Papers 2192, Cowles Foundation for Research in Economics, Yale University.
    5. Lee, Taehyun & Moutzouris, Ioannis C & Papapostolou, Nikos C & Fatouh, Mahmoud, 2023. "Foreign exchange hedging using regime-switching models: the case of pound sterling," Bank of England working papers 1042, Bank of England.
    6. Lee, Sokbae & Liao, Yuan & Seo, Myung Hwan & Shin, Youngki, 2021. "Sparse HP filter: Finding kinks in the COVID-19 contact rate," Journal of Econometrics, Elsevier, vol. 220(1), pages 158-180.
    7. Jylhä, Petri & Lof, Matthijs, 2022. "Mind the Basel gap," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 79(C).
    8. Hiroshi Yamada, 2023. "Quantile regression version of Hodrick–Prescott filter," Empirical Economics, Springer, vol. 64(4), pages 1631-1645, April.
    9. Peter C. B. Phillips & Sainan Jin, 2021. "Business Cycles, Trend Elimination, And The Hp Filter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(2), pages 469-520, May.
    10. Hiroshi Yamada & Ruoyi Bao, 2022. "$$\ell _{1}$$ ℓ 1 Common Trend Filtering," Computational Economics, Springer;Society for Computational Economics, vol. 59(3), pages 1005-1025, March.
    11. Kristian Jönsson, 2020. "Cyclical Dynamics and Trend/Cycle Definitions: Comparing the HP and Hamilton Filters," Journal of Business Cycle Research, Springer;Centre for International Research on Economic Tendency Surveys (CIRET), vol. 16(2), pages 151-162, November.
    12. Ziwei Mei & Peter C. B. Phillips & Zhentao Shi, 2022. "The boosted HP filter is more general than you might think," Papers 2209.09810, arXiv.org.
    13. Wolf, Elias & Mokinski, Frieder & Schüler, Yves, 2020. "On adjusting the one-sided Hodrick-Prescott filter," Discussion Papers 11/2020, Deutsche Bundesbank.

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