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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Yamada Hiroshi & Jahra Fatima Tuj, 2019. "An explicit formula for the smoother weights of the Hodrick–Prescott filter," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 23(5), pages 1-10, December.
  • Handle: RePEc:bpj:sndecm:v:23:y:2019:i:5:p:10:n:1
    DOI: 10.1515/snde-2018-0035
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    More about this item

    Keywords

    hodrick–prescott filter; pentadiagonal toeplitz matrix; smoother weights; whittaker–henderson method of graduation; 62G05;
    All these keywords.

    JEL classification:

    • 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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