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

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Publication details

JournalReview of economics and statistics
DateAccepted/In press - 25 Jan 2016
DatePublished (current) - 2 May 2017
Issue number2
Number of pages5
Pages (from-to)314-318
Original languageEnglish


We derive the exact expression for the weights of the Hodrick-Prescott (HP)
filter in finite sample without making any assumptions about the statistical
properties of the time series. We use the results to give insights about 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.

Bibliographical note

© by the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Embargo period: 12 months. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy.

    Research areas

  • trend component; cyclical component; smoothing parameter; Sherman-Morrison.

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