Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-28T02:48:00.278Z Has data issue: false hasContentIssue false
  • English
  • Français

Graduation by dynamic regression methods

Published online by Cambridge University Press:  20 April 2012

R. J. Verrall
R. J. Verrall
Affiliation:
The City University, London
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper extends the theory of graduation by parametric formulae to include dynamic estimation methods. This is an application of the Kalman filter and allows the parameters of the curve fitted to vary with age. The amount of variation is determined by the amount of smoothing required, and the method can be regarded as a combination of curve fitting and sequential smoothing, each of which has been used separately for performing graduations. In practice, a dynamic straight line can always be used for the graduation and the method has a sensible logical interpretation.

Keywords

GraduationKalman FilterLinear ModelsMortality
Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 120 , Issue 1 , 1993 , pp. 153 - 170
Copyright
Copyright © Institute and Faculty of Actuaries 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Baker, R. J. & Nelder, J. A. (1978). GLIM Release 3. Nag, Oxford.Google Scholar
Benjamin, B. & Pollard, J. H. (1980). The Analysis of Mortality and Other Actuarial Statistics. Heinemann, London.Google Scholar
C.M.I. Committee: (1976). The Graduation of Pensioners’ and of Annuitants’ Mortality Experience, 1967–70, CMIR, 2, 57.Google Scholar
Copas, J. H. & Haberman, S. (1983). Non-Parametric Graduation using Kernel Methods. J.I.A. 110, 135.Google Scholar
Durbin, J. (1990). Extensions of Kalman Modelling to non-Gaussian Observations. Quaderni di Stat. e Math. Applic. alle Scienze Econ. Sociali, XII, 1, 3.Google Scholar
Forfar, D. O., McCutcheon, J. J. & Wilkie, A. D. (1988). On Graduation by Mathematical Formula. J.I.A. 115, 1 and T.F.A. 41, 97.Google Scholar
McCullagh, P. & Nelder, J. R. (1989). Ganeralised Linear Models, 2nd ed. Chapman and Hall.CrossRefGoogle Scholar
Renshaw, A. E. (1991) Actuarial Graduation Practice and Generalised Linear and Non-Linear Models. J.I.A. 118, 295.Google Scholar
West, M., Harrison, P. J. & Migon, H. S. (1985). Dynamic Generalised Linear Models and Hayesian Forecasting, with discussion. J. American Statist. Ass., 80, 73.CrossRefGoogle Scholar