Models of mortality rates – analysing the residuals

ABSTRACT

The area of mortality modelling has received significant attention over the last 25 years owing to the need to quantify and forecast improving mortality rates. This need is driven primarily by the concern of governments, insurance and actuarial professionals and individuals to be able to fund their old age. In particular, to quantify the costs of increasing longevity we need suitable model of mortality rates that capture the dynamics of the data and forecast them with sufficient accuracy to make them useful. In this article, we test several of the leading time series models by considering the fitting quality and in particular, testing the residuals of those models for normality properties. In a wide ranging study considering 30 countries we find that almost exclusively the residuals do not demonstrate normality. Further, in Hurst tests of the residuals we find evidence that structure remains that is not captured by the models.

KEYWORDS:

• Mortality
• stochastic models
• residuals
• Hurst exponents

JEL CLASSIFICATION:

• C51
• C52
• G22
• G23
• J11

Acknowledgements

A version of this article was presented at the IME Congress in Shanghai in 2014, the authors are grateful for the comments received.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ This can be found at http://www.mortality.org/. The database is maintained in the Department of Demography at the University of California, Berkeley, USA, and at the Max Planck Institute for Demographic Research in Rostock, Germany.

² The open-source coding used can be found at http://www.macs.hw.ac.uk/ andrewc/lifemetrics/

Additional information

Funding

This work was supported by the ARC Linkage [LP160101038];