Outlier analysis and mortality forecasting: The United Kingdom and Scandinavian countries

Abstract

The Lee-Carter model and its variants have been extensively employed by actuaries, demographers, and many others to forecast age-specific mortality. In this study, we use mortality data from England and Wales, and four Scandinavian countries to perform time-series outlier analysis of the key component of the Lee-Carter model – the mortality index. We begin by employing a systematic outlier detection process to ascertain the timing, magnitude, and persistence of any outliers present in historical mortality trends. We then try to match the identified outliers with imperative events that could possibly justify the vacillations in human mortality levels. At the same time, we adjust the effect of the outliers for model re-estimation. A new iterative model re-estimation method is proposed to reduce the chance of erroneous model specification. The empirical results indicate that the outlier-adjusted model could achieve more efficient forecasts of variables such as death rates and life expectancies. Finally, we point out that the Lee-Carter forecasts are especially vulnerable to outliers near the forecast origin, and discuss the potential limitations of the application of the Lee-Carter model to mortality forecasting.

Keywords:

• Lee-Carter model
• Life expectancy
• Outlier detection
• Time-series analysis

Acknowledgments

The authors are indebted to the editor and an anonymous referee for their helpful comments on an earlier version of the article. The authors are also grateful to the Human Mortality Database (www.mortality.org/ www.humanmortality.de) and the Office of National Statistics in the United Kingdom for providing the data used in this study. This work was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region (Competitive Earmarked Research Grant Project No. HKU 7111/01H).

Notes

Note: the outlier adjusted k _t can be computed by reconciling the unadjusted k _t with the type and magnitude of the detected outliers provided in Table 2 in the main text.