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Boosted Whittaker–Henderson Graduation

Author

Listed:
  • Zihan Jin

    (Graduate School of Humanities and Social Sciences, Hiroshima University, 1-2-1 Kagamiyama, Higashi-Hiroshima 739-8525, Japan)

  • Hiroshi Yamada

    (Graduate School of Humanities and Social Sciences, Hiroshima University, 1-2-1 Kagamiyama, Higashi-Hiroshima 739-8525, Japan)

Abstract

The Whittaker–Henderson (WH) graduation is a smoothing method for equally spaced one-dimensional data such as time series. It includes the Bohlmann filter, the Hodrick–Prescott (HP) filter, and the Whittaker graduation as special cases. Among them, the HP filter is the most prominent trend-cycle decomposition method for macroeconomic time series such as real gross domestic product. Recently, a modification of the HP filter, the boosted HP (bHP) filter, has been developed, and several studies have been conducted. The basic idea of the modification is to achieve more desirable smoothing by extracting long-term fluctuations remaining in the smoothing residuals. Inspired by the modification, this paper develops the boosted version of the WH graduation, which includes the bHP filter as a special case. Then, we establish its properties that are fundamental for applied work. To investigate the properties, we use a spectral decomposition of the penalty matrix of the WH graduation

Suggested Citation

  • Zihan Jin & Hiroshi Yamada, 2024. "Boosted Whittaker–Henderson Graduation," Mathematics, MDPI, vol. 12(21), pages 1-18, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:21:p:3377-:d:1508776
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    References listed on IDEAS

    as
    1. 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.
    2. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
    3. Peter Phillips, 2010. "Two New Zealand pioneer econometricians," New Zealand Economic Papers, Taylor & Francis Journals, vol. 44(1), pages 1-26.
    4. Yamada, Hiroshi, 2020. "A Smoothing Method That Looks Like The Hodrick–Prescott Filter," Econometric Theory, Cambridge University Press, vol. 36(5), pages 961-981, October.
    5. Weinert, Howard L., 2007. "Efficient computation for Whittaker-Henderson smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 959-974, October.
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