A note on Whittaker-Henderson graduation: Bisymmetry of the smoother matrix

Whittaker-Henderson (WH) graduation is a popular smoothing method that has been used for mortality table construction in the actuarial sciences and for the trend-cycle decomposition in time series econometrics. This paper proves that the smoother matrix of WH graduation is bisymmetric (i.e., symmetr...

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Bibliographic Details
Published in:	Communications in statistics. Theory and methods Vol. 49; no. 7; pp. 1629 - 1634
Main Author:	Yamada, Hiroshi
Format:	Journal Article
Language:	English
Published:	Philadelphia Taylor & Francis 02-04-2020 Taylor & Francis Ltd
Subjects:	bisymmetry C221 centrosymmetry Econometrics Hodrick-Prescott filter Mathematical analysis Matrix methods smoother matrix Whittaker-Henderson graduation
Online Access:	Get full text
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Summary:	Whittaker-Henderson (WH) graduation is a popular smoothing method that has been used for mortality table construction in the actuarial sciences and for the trend-cycle decomposition in time series econometrics. This paper proves that the smoother matrix of WH graduation is bisymmetric (i.e., symmetric centrosymmetric). This result implies, for example, that the first row of the smoother matrix is equivalent to the last row of it in reverse order. We also provide some related results.
ISSN:	0361-0926 1532-415X
DOI:	10.1080/03610926.2018.1563183