{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T02:50:20Z","timestamp":1783997420580,"version":"3.55.0"},"reference-count":49,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2020,3,23]],"date-time":"2020-03-23T00:00:00Z","timestamp":1584921600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2020,10]]},"abstract":"<jats:p>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\u2013Prescott (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 M\u00fcller and Watson (2018, <jats:italic>Econometrica<\/jats:italic> 86, 775\u2013804). 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.<\/jats:p>","DOI":"10.1017\/s0266466619000379","type":"journal-article","created":{"date-parts":[[2020,3,23]],"date-time":"2020-03-23T05:00:37Z","timestamp":1584939637000},"page":"961-981","source":"Crossref","is-referenced-by-count":21,"title":["A SMOOTHING METHOD THAT LOOKS LIKE THE HODRICK\u2013PRESCOTT FILTER"],"prefix":"10.1017","volume":"36","author":[{"given":"Hiroshi","family":"Yamada","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2020,3,23]]},"reference":[{"key":"S0266466619000379_r14","doi-asserted-by":"publisher","DOI":"10.1198\/073500101681019909"},{"key":"S0266466619000379_r49","first-page":"1","article-title":"An explicit formula for the smoother weights of the Hodrick\u2013Prescott filter","volume":"23","author":"Yamada","year":"2019","journal-title":"Studies in Nonlinear Dynamics and Econometrics"},{"key":"S0266466619000379_r28","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1991.10475089"},{"key":"S0266466619000379_r29","doi-asserted-by":"publisher","DOI":"10.2307\/2999618"},{"key":"S0266466619000379_r33","doi-asserted-by":"publisher","DOI":"10.2139\/ssrn.2622477"},{"key":"S0266466619000379_r36","volume-title":"A Matrix Handbook for Statisticians","author":"Seber","year":"2008"},{"key":"S0266466619000379_r24","volume-title":"Chebyshev Polynomials","author":"Mason","year":"2003"},{"key":"S0266466619000379_r41","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2006.11.038"},{"key":"S0266466619000379_r18","first-page":"29","article-title":"A new method of graduation","volume":"25","author":"Henderson","year":"1924","journal-title":"Transactions of the Actuarial Society of America"},{"key":"S0266466619000379_r43","first-page":"105","article-title":"A note on bandpass filters based on the Hodrick\u2013Prescott filter and the OECD system of composite leading indicators","volume":"2011","author":"Yamada","year":"2012","journal-title":"OECD Journal: Journal of Business Cycle Measurement and Analysis"},{"key":"S0266466619000379_r35","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466619000331"},{"key":"S0266466619000379_r39","doi-asserted-by":"publisher","DOI":"10.1137\/120897572"},{"key":"S0266466619000379_r7","doi-asserted-by":"publisher","DOI":"10.1162\/REST_a_00594"},{"key":"S0266466619000379_r17","doi-asserted-by":"publisher","DOI":"10.2307\/2526316"},{"key":"S0266466619000379_r25","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA15047"},{"key":"S0266466619000379_r22","doi-asserted-by":"publisher","DOI":"10.1137\/070690274"},{"key":"S0266466619000379_r34","doi-asserted-by":"publisher","DOI":"10.2139\/ssrn.3447546"},{"key":"S0266466619000379_r27","doi-asserted-by":"publisher","DOI":"10.1080\/03461238.2010.534257"},{"key":"S0266466619000379_r3","volume-title":"Proceedings of the Symposium on Time Series Analysis","author":"Anderson","year":"1963"},{"key":"S0266466619000379_r38","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144598336745"},{"key":"S0266466619000379_r45","doi-asserted-by":"publisher","DOI":"10.1080\/03610926.2017.1285934"},{"key":"S0266466619000379_r8","doi-asserted-by":"publisher","DOI":"10.1016\/0014-2921(89)90035-4"},{"key":"S0266466619000379_r30","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466605050085"},{"key":"S0266466619000379_r20","doi-asserted-by":"publisher","DOI":"10.2307\/2953682"},{"key":"S0266466619000379_r6","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00319"},{"key":"S0266466619000379_r1","doi-asserted-by":"publisher","DOI":"10.1109\/T-C.1974.223784"},{"key":"S0266466619000379_r19","first-page":"52","article-title":"Further remarks on graduation","volume":"26","author":"Henderson","year":"1925","journal-title":"Transactions of the Actuarial Society of America"},{"key":"S0266466619000379_r42","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091500077853"},{"key":"S0266466619000379_r15","doi-asserted-by":"publisher","DOI":"10.1162\/rest_a_00706"},{"key":"S0266466619000379_r32","doi-asserted-by":"publisher","DOI":"10.1080\/00779951003614057"},{"key":"S0266466619000379_r11","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/38.1-2.159"},{"key":"S0266466619000379_r31","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2005.02.010"},{"key":"S0266466619000379_r23","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-1889(06)80010-2"},{"key":"S0266466619000379_r10","first-page":"409","article-title":"Testing for serial correlation in least squares regression. 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