An explicit formula for the smoother weights of the Hodrick–Prescott filter-Reference-Cited by-同舟云学术

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

Published:2019-01-23 Issue:5 Volume:23 Page:
ISSN:1558-3708
Container-title:Studies in Nonlinear Dynamics & Econometrics
language:en
Short-container-title:

Author:

Yamada Hiroshi¹,Jahra Fatima Tuj²

Affiliation:

1. 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

2. Graduate School of Social Sciences , Hiroshima University , Higashi-Hiroshima 739-8525 , Japan

Abstract

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.

Funder

Japan Society for the Promotion of Science

Publisher

Walter de Gruyter GmbH

Subject

Economics and Econometrics,Social Sciences (miscellaneous),Analysis,Economics and Econometrics,Social Sciences (miscellaneous),Analysis

Link

https://www.degruyter.com/document/doi/10.1515/snde-2018-0035/pdf

Reference24 articles.

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2. Bierens, H. 1997. “Testing the Unit Root with Drift Hypothesis Against Nonlinear Trend Stationarity, with an Application to the U.S. Price Level and Interest Rate.” Journal of Econometrics 81: 29–64.

3. Cornea-Madeira, A. 2017. “The Explicit Formula for the Hodrick–Prescott Filter in Finite Sample.” Review of Economics and Statistics 99 (2): 314–318.

4. Craven, P., and G. Wahba. 1979. “Smoothing Noisy Data with Spline Functions: Estimating the Correct Degree of Smoothing by the Method of Generalized Cross-Validation.” Numerical Mathematics 31: 377–403.

5. De Jong, R. M., and N. Sakarya. 2016. “The Econometrics of the Hodrick–Prescott Filter.” Review of Economics and Statistics 98 (2): 310–317.

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