A modification of the Whittaker–Henderson method of graduation

Abstract

This paper presents a modified Whittaker–Henderson (WH) Method of Graduation. After giving a closed-form solution, we show that it is of practical use because it provides not only a smoothed series identical to that of the WH graduation, but also an extrapolation beyond the sample limit of current data. In addition, we introduce two other penalized least squares problems and show that they provide the same results as those of the modified WH graduation.

Keywords:

• Whittaker–Henderson method of graduation
• hodrick–prescott filter
• penalized least squares

Mathematics Subject Classification:

• 62G05

Acknowledgements

We thank an anonymous referee for his/her valuable suggestions and comments. The usual caveat applies.

Additional information

Funding

This work was supported in part by Japan Society for the Promotion of Science KAKENHI Grant No. 16H03606.