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Several least-squares problems related to the Hodrick–Prescott filtering

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  • Hiroshi Yamada

Abstract

The Hodrick–Prescott (HP) filtering is frequently used in macroeconometrics to decompose time series, such as real gross domestic product, into their trend and cyclical components. Because the HP filtering is a basic econometric tool, it is necessary to have a precise understanding of the nature of it. This article contributes to the literature by listing several (penalized) least-squares problems that are related to the HP filtering, three of which are newly introduced in the article, and showing their properties. We also remark on their generalization.

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  • Hiroshi Yamada, 2018. "Several least-squares problems related to the Hodrick–Prescott filtering," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(5), pages 1022-1027, March.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:5:p:1022-1027
    DOI: 10.1080/03610926.2017.1285934
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    Cited by:

    1. Hiroshi Yamada, 2023. "Quantile regression version of Hodrick–Prescott filter," Empirical Economics, Springer, vol. 64(4), pages 1631-1645, April.
    2. Ruixue Du & Hiroshi Yamada, 2020. "Principle of Duality in Cubic Smoothing Spline," Mathematics, MDPI, vol. 8(10), pages 1-19, October.

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