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A SMOOTHING METHOD THAT LOOKS LIKE THE HODRICK–PRESCOTT FILTER

Published online by Cambridge University Press:  23 March 2020

Hiroshi Yamada
Hiroshi Yamada*
Affiliation:
Hiroshima University
*
Address correspondence to Hiroshi Yamada, 1-2-1 Kagamiyama, Higashi-Hiroshima 739-8525, Japan; e-mail: yamada@hiroshima-u.ac.jp.
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Abstract

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In recent decades, in the research community of macroeconometric time series analysis, we have observed growing interest in the smoothing method known as the Hodrick–Prescott (HP) filter. This article examines the properties of an alternative smoothing method that looks like the HP filter, but is much less well known. We show that this is actually more like the exponential smoothing filter than the HP filter although it is obtainable through a slight modification of the HP filter. In addition, we also show that it is also like the low-frequency projection of Müller and Watson (2018, Econometrica 86, 775–804). We point out that these results derive from the fact that all three similar smoothing methods can be regarded as a type of graph spectral filter whose graph Fourier transform is discrete cosine transform. We then theoretically reveal the relationship between the similar smoothing methods and provide a way of specifying the smoothing parameter that is necessary for its application. An empirical examination illustrates the results.

Type
ARTICLES
Information
Econometric Theory , Volume 36 , Issue 5 , October 2020 , pp. 961 - 981
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Footnotes

I am grateful to In Choi, Chirok Han, Eiji Kurozumi, Takashi Yamagata, Daisuke Yamazaki, three anonymous referees, and the editor, Peter C.B. Phillips, for their valuable suggestions and comments. I also thank the participants in several conferences including the York–Hiroshima Joint Symposium 2018 held at the University of York, the BK21PLUS Korean Economic Group International Conference on Econometrics held at Korea University, and the SH3 Conference on Econometrics 2019 held at Singapore Management University. In addition, I appreciate the kindness of Ulrich K. Müller and Mark W. Watson in providing their dataset and m files. The usual caveat applies. The Japan Society for the Promotion of Science supported this work through KAKENHI Grant No. 16H03606.

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