An explicit formula for the smoother weights of the Hodrick–Prescott filter

Yamada Hiroshi () and Jahra Fatima Tuj
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Yamada Hiroshi: Graduate School of Social Sciences, Hiroshima University, 1-2-1 Kagamiyama,Higashi-Hiroshima 739-8525, Japan, Phone: +81-82-424-7214; Fax: +81-82-424-7212
Jahra Fatima Tuj: Graduate School of Social Sciences, Hiroshima University, Higashi-Hiroshima 739-8525, Japan

Studies in Nonlinear Dynamics & Econometrics, 2019, vol. 23, issue 5, 10

Abstract: By applying the Sherman–Morrison–Woodbury (SMW) formula and a discrete cosine transformation matrix, De Jong and Sakarya [De Jong, R. M., and N. Sakarya. 2016. “The Econometrics of the Hodrick–Prescott Filter.” Review of Economics and Statistics 98 (2): 310–317] recently derived an explicit formula for the smoother weights of the Hodrick–Prescott filter. More recently, by applying the SMW formula and the spectral decomposition of a symmetric tridiagonal Toeplitz matrix, Cornea-Madeira [Cornea-Madeira, A. 2017. “The Explicit Formula for the Hodrick–Prescott Filter in Finite Sample.” Review of Economics and Statistics 99: 314–318] provided a simpler formula. This paper provides an alternative simpler formula for it and explains the reason why our approach leads to a simpler formula.

Keywords: hodrick–prescott filter; pentadiagonal toeplitz matrix; smoother weights; whittaker–henderson method of graduation (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1515/snde-2018-0035

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