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HPX filter: a hybrid of Hodrick–Prescott filter and multiple regression

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  • Yamada Hiroshi

    (Graduate School of Humanities and Social Sciences, Hiroshima University, Higashi-Hiroshima, Japan)

Abstract

This paper considers an extension of Hodrick–Prescott (HP) filter. It is a hybrid of HP filter and multiple regression. We refer to the filter as “HPX filter”. It is well known that HP filter has a unique global minimizer and the solution can be represented in matrix notation explicitly. Does HPX filter also have a unique global minimizer? Is it accomplished without any additional assumptions? Can the solution be expressed in matrix notation explicitly? In this paper, we answer these questions. In addition, this paper (i) provides an alternative perspective on the filter by representing it as a generalized ridge regression and (ii) gives an extension of it, which is a hybrid of Whittaker–Henderson method of graduation and multiple regression.

Suggested Citation

  • Yamada Hiroshi, 2024. "HPX filter: a hybrid of Hodrick–Prescott filter and multiple regression," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 28(4), pages 661-671.
    • Handle: RePEc:bpj:sndecm:v:28:y:2024:i:4:p:661-671:n:1006
    DOI: 10.1515/snde-2023-0004
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    More about this item

    Keywords

    cubic smoothing spline; generalized ridge regression; Hodrick–Prescott filter; multiple regression; Whittaker–Henderson method of graduation;
    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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