Abstract
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.
2010 Mathematics Subject Classification:
JEL Classification:
Acknowledgments
The author thanks an anonymous referee for his/her valuable comments. The usual caveat applies.
Notes
1 These matrices are equivalent for p = 1, 2.
2 Although the corollaries of Proposition 3.1 corresponding to Corollaries 2.3 and 2.4 are also obtainable, they are omitted to save space.