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

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

Studies in Nonlinear Dynamics & Econometrics, 2024, vol. 28, issue 4, 661-671

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.

Keywords: cubic smoothing spline; generalized ridge regression; Hodrick–Prescott filter; multiple regression; Whittaker–Henderson method of graduation (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1515/snde-2023-0004

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