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

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  • Hiroshi Yamada
    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
  • Fatima Tuj Jahra
    Graduate School of Social Sciences , Hiroshima University , Higashi-Hiroshima 739-8525 , Japan

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<jats:title>Abstract</jats:title> <jats:p>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.” <jats:italic>Review of Economics and Statistics</jats:italic> 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.” <jats:italic>Review of Economics and Statistics</jats:italic> 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.</jats:p>

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